Holdings: The quantum theory of fields

The quantum theory of fields: 3 Supersymmetry

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Bibliographic Details
Main Author:	Weinberg, Steven 1933-2021 (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2005
Edition:	Paperback ed.
Subjects:	Quantenfeldtheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XXII, 419 S.
ISBN:	0521670551 9780521670555

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adam_text	Contents Sections marked with an asterisk are somewhat out of the book s main line of development and may be omitted in a first reading. PREFACE TO VOLUME III xvi NOTATION xx 24 HISTORICAL INTRODUCTION 1 24.1 Unconventional Symmetries and No-Go Theorems 1 SU(6) symmetry Q Elementary no-go theorem for unconventional semi-simple compact Lie algebras Π Role of relativity 24.2 The Birth of Supersymmetry 4 Bosonic string theory α Fermionic coordinates D Worldsheet supersymmetry О Wess-Zumino model Π Precursors Appendix A S t/(6) Symmetry of Non-Relativistic Quark Models 8 Appendix В The Coleman-Mandula Theorem 12 Problems 22 References 22 25 SUPERSYMMETRY ALGEBRAS 25 25.1 Graded Lie Algebras and Graded Parameters 25 Fermionic and bosonic generators Π Super-Jacobi identity О Grassmann par¬ ameters G Structure constants from supergroup multiplication rules □ Complex conjugates 25.2 Supersymmetry Algebras 29 Haag-Lopuszanski-Sohnius theorem □ Lorentz transformation of fermionic gen¬ erators □ Central charges О Other bosonic symmetries D Я -symmetry D Simple vii viii Contents and extended supersymmetry D Four-component notation о Superconformai algebra 25.3 Space Inversion Properties of Supersymmetry Generators 40 Parity phases in simple supersymmetry □ Fermions have imaginary parity О Parity matrices in extended supersymmetry O Dirac notation 25.4 Massless Particle Supermultiplets 43 Known particles are massless for unbroken supersymmetry □ Helicity raising and lowering operators Q Simple supersymmetry doublets D Squarks, sleptons, and gauginos □ Gravitino Π Extended supersymmetry multiplets α Chirality problem for extended supersymmetry 25.5 Massive Particle Supermultiplets 48 Raising and lowering operators for spin 3-component О General massive multi¬ plets for simple supersymmetry D Collapsed supermultiplet D Mass bounds in extended supersymmetry О BPS states and short supermultiplets Problems 53 References 54 26 SUPERSYMMETRIC FIELD THEORIES 55 26.1 Direct Construction of Field Supermultiplets 55 Construction of simplest N = 1 field multiplet О Auxiliary field □ Infinitesi¬ mal supersymmetry transformation rules D Four-component notation ü Wess- Zumino supermultiplets regained 26.2 General Superfields 59 Superspace spinor coordinates О Supersymmetry generators as superspace dif¬ ferential operators π Supersymmetry transformations in superspace □ General superfields □ Multiplication rales □ Supersymmetric differential operators in su¬ perspace □ Supersymmetric actions for general superfields □ Parity of component fields □ Counting fermionic and bosonic components 26.3 Chiral and Linear Superfields 68 Chirality conditions on a general superfield D Left- and right-chiral superfields ü Coordinates χμ± D Differential constraints □ Product rules □ Supersymmetric &- terms α J^-terms equivalent to D-terms α Superpotentials G Kahler potentials ü Partial integration in superspace G Space inversion of chiral superfields □ .R-symmetry again D Linear superfields 26.4 Renormalizable Theories of Chiral Superfields 75 Counting powers о Kinematic Lagrangian D J^-term of the superpotential □ Complete Lagrangian D Elimination of auxiliary fields □ On-shell superalgebra π Vacuum solutions □ Masses and couplings □ Wess-Zumino Lagrangian regained Contents ix 26.5 Spontaneous Snpersymmetry Breaking in the Tree Approximation 83 O Raifeartaigh mechanism □ R-symmetry constraints π Flat directions □ Gold- stino 26.6 Superspace Integrals, Field Equations, and the Current Superitela 86 Berezin integration D D- and J^-terms as superspace integrals G Potential su- perfields Π Superspace field equations π Conserved currents as components of linear superfields □ Conservation conditions in superspace 26.7 The Supercurrent 90 Supersymmetry current α Superspace transformations generated by the super- symmetry current □ Local supersymmetry transformations Π Construction of the supercurrent D Conservation of the supercurrent D Energy-momentum ten¬ sor and R-current Π Scale invariance and R conservation □ Non-uniqueness of supercurrent 26.8 General Kahler Potentials* 102 Non-renormalizable non-derivative actions □ D-term of Kahler potential □ Kahler metric О Lagrangian density □ Non-linear σ -models from spontaneous internal symmetry breaking □ Kahler manifolds □ Complexified coset spaces Appendix Majorana Spinors 107 Problems 111 References 112 27 SUPERSYMMETRIC GAUGE THEORIES 113 27.1 Gauge-Invariant Actions for Chiral Superfields 113 Gauge transformation of chiral superfields Π Gauge superfield V □ Extended gauge invariance □ Wess-Zumino gauge □ Supersymmetric gauge-invariant kine¬ matic terms for chiral superfields 27.2 Gauge-Invariant Action for Abelian Gauge Superfields 122 Field strength supermultiplet Π Kinematic Lagrangian density for Abelian gauge supermultiplet D Fayet-Iliopoulos terms о Abelian field-strength spinor super- field Wx □ Left- and right-chiral parts of Wx □ Wx as a superspace derivative of V □ Gauge invariance of W% □ Bianchi identities in superspace 27.3 Gauge-Invariant Action for General Gauge Superfields 127 Kinematic Lagrangian density for non-Abelian gauge supermultiplet α Νοη- Abelian field-strength spinor superfield Wąx D Left- and right-chiral parts of □ 6-term D Complex coupling parameter τ ПА Renormalizable Gauge Theories with Chiral Superfields 132 Supersymmetric Lagrangian density □ Elimination of auxiliary fields О Condi¬ tions for unbroken supersymmetry О Counting independent conditions and field x Contents variables О Unitarity gauge Π Masses for spins 0, 1/2, and 1 □ Supersymmetry current О Non-Abelian gauge theories with general Kahler potentials □ Gaugino mass 27.5 Snpersymmetry Breaking in the Tree Approximation Resumed 144 Supersymmetry breaking in supersymmetric quantum electrodynamics □ General case: masses for spins 0, 1/2, and 1 □ Mass sum rule α Goldstino component of gaugino and chiral fermion fields 27.6 Perturbative Non-Renormalization Theorems 148 Non-renormalization of Wilsonian superpotential Π One-loop renormalization of terms quadratic in gauge superfields Π Proof using holomorphy and new symmetries with external superfields О Non-renormalization of Fayet-Iliopoulos constants ξά D For ξΛ = 0, supersymmetry breaking depends only on super- potential O Non-renormalizable theories 27.7 Soft Supersymmetry Breaking* 155 Limitation on supersymmetry-breaking radiative corrections D Quadratic diver¬ gences in tadpole graphs 27.8 Another Approach: Gauge-Invariant Supersymmetry Transformations 157 De Wit-Freedman transformation rules О Preserving Wess-Zumino gauge with combined supersymmetry and extended gauge transformations 27.9 Gauge Theories with Extended Supersymmetry* 160 N = 2 supersymmetry from N — 1 supersymmetry and .R-symmetry D La- grangian for N = 2 supersymmetric gauge theory D Eliminating auxiliary fields □ Supersymmetry currents □ Witten-Olive calculation of central charge O Non- renormalization of masses D BPS monopoles π Adding hypermultiplets G N = 4 supersymmetry Π Calculation of beta function D N = 4 theory is finite □ Montonen-Olive duality Problems 175 References 176 28 SUPERSYMMETRIC VERSIONS OF THE STANDARD MODEL 179 28.1 Superfields, Anomalies, and Conservation Laws 180 Quark, lepton, and gauge superfields D At least two scalar doublet superfields D J^-term Yukawa couplings D Constraints from anomalies □ Unsuppressed violation of baryon and lepton numbers D R-symmetry D R parity О /¿-term □ Hierarchy problem D Sparticle masses D Cosmological constraints on lightest superparticle 28.2 Supersymmetry and Strong-Electroweak Unification 188 Renormalization group equations for running gauge couplings □ Effect of super- Contents xi symmetry on beta functions □ Calculation of weak mixing angle and unification mass Π Just two scalar doublet superfields □ Coupling at unification scale 28.3 Where is Supersymmetry Broken? 192 Tree approximation supersymmetry breakdown ruled out D Hierarchy from non- perturbative effects of asymptotically free gauge couplings □ Gauge and grav¬ itational mediation of supersymmetry breaking α Estimates of supersymmetry- breaking scale Π Gravitino mass □ Cosmological constraints 28.4 The Minimal Supersymmetric Standard Model 198 Supersymmetry breaking by superrenormalizable terms □ General Lagrangian О Flavor changing processes □ Calculation of K° <-»· К □ Degenerate squarks and sleptons D CP violation D Calculation of quark chromoelectric dipole moment □ Naive dimensional analysis □ Neutron electric dipole moment □ Constraints on masses and/or phases 28.5 The Sector of Zero Baryon and Lepton Number 209 D-term contribution to scalar potential D /¿-term contribution to scalar poten¬ tial □ Soft supersymmetry breaking terms □ Vacuum stability constraint on parameters α Finding a minimum of potential □ Βμ φ 0 Π Masses of CP-odd neutral scalars □ Masses of CP-even neutral scalars □ Masses of charged scalars D Bounds on masses □ Radiative corrections ü Conditions for electroweak symmetry breaking G Charginos and neutralinos D Lower bound on ΙμΙ 28.6 Gauge Mediation of Supersymmetry Breaking 220 Messenger superfields Q Supersymmetry breaking in gauge supermultiplet prop¬ agators D Gaugino masses □ Squark and slepton masses Π Derivation from holomorphy □ Radiative corrections о Numerical examples D Higgs scalar masses Π μ problem D Ац and Су parameters Π Gravitino as lightest sparticle О Next-to-lightest sparticle 28.7 Baryon and Lepton Non-Conservation 235 Dimensionality five interactions о Gaugino exchange О Gluino exchange sup¬ pressed D Wino and bino exchange effects Π Estimate of proton lifetime □ Favored modes of proton decay Problems 240 References 241 29 BEYOND PERTURBATION THEORY 248 29.1 General Aspects of Supersymmetry Breaking 248 Finite volume α Vacuum energy and supersymmetry breaking D Partially broken extended supersymmetry? □ Pairing of bosonic and fermionic states □ Pairing of vacuum and one-goldstino state O Witten index О Supersymmetry unbroken xii Contents in the Wess-Zumino model D Models with unbroken supersymmetry and zero Witten index D Large field values D Weighted Witten indices 29.2 Supersymmetry Current Sum Rules 256 Sum rale for vacuum energy density □ One-goldstino contribution □ The supersymmetry-breaking parameter F □ Soft goldstino amplitudes □ Sum rule for supersymmetry current-fermion spectral functions □ One-goldstino contribu¬ tion □ Vacuum energy density in terms of êF and D vacuum values D Vacuum energy sum rule for infinite volume 29.3 Non-Perturbative Corrections to the Superpotential 266 Non-perturbative effects break external field translation and R-conservation D Remaining symmetry О Example: generalized supersymmetric quantum chromo- dynamics Π Structure of induced superpotential for Ci > Сг О Stabilizing the vacuum with a bare superpotential □ Vacuum moduli in generalized supersym¬ metric quantum chromodynamics for Nc > Nf □ Induced superpotential is linear in bare superpotential parameters for Q = Сг □ One-loop renormalization of term for all Cu C2 29.4 Supersymmetry Breaking in Gauge Theories 276 Witten index vanishes in supersymmetric quantum electrodynamics D C-weighted Witten index О Supersymmetry unbroken in supersymmetric quantum electro¬ dynamics G Counting zero-energy gauge field states in supersymmetric quantum electrodynamics О Calculating Witten index for general supersymmetric pure gauge theories О Counting zero-energy gauge field states for general supersym¬ metric pure gauge theories α Weyl invariance D Supersymmetry unbroken in general supersymmetric pure gauge theories D Witten index and R anomalies Π Adding chiral scalars Π Model with spontaneously broken supersymmetry 29.5 The Seiberg-Witten Solution* 287 Underlying N = 2 supersymmetric Lagrangian □ Vacuum modulus Π Leading non-renormalizable terms in the eifective Lagrangian □ Effective Lagrangian for component fields Π Kahler potential and gauge coupling from a function й(Ф) □ S 1/(2) R-symmetry D Prepotential □ Duality transformation □ й(Ф) translation D Z<¡ R-symmetry D SL(2,Z)-symmetry D Central charge D Charge and magnetic monopole moments D Perturbative behavior for large a □ Monodromy at infinity Π Singularities from dyons □ Monodromy at singularities Π Seiberg- Witten solution π Uniqueness proof Problems 3Q5 References 305 3β SUPERGRAPHS 307 ЗОЛ Potential Superfields ЗО8 Contents xiii Problem of chiral constraints □ Corresponding problem in quantum electro¬ dynamics D Path integrals over potential superfields 30.2 Superpr opagators 310 A troublesome invariance □ Change of variables □ Defining property of super- propagator □ Analogy with quantum electrodynamics ü Propagator for potential superfields О Propagator for chiral superfields 30.3 Calculations with Supergraphs 313 Superspace quantum effective action α Locality in fermionic coordinates α D- terms and J^-terms in effective action □ Counting superspace derivatives □ No renormalization of J^terms Problems 316 References 316 31 SUPERGRAVITY 318 31.1 The Metric Superfield 319 Vierbein formalism О Transformation of gravitational field □ Transformation of gravitino field Q Generalized transformation of metric superfield Ημ □ Interaction of Η џ with supercurrent Π Invariance of interaction □ Generalized transformation of Ημ components О Auxiliary fields □ Counting components Π Interaction of Ημ component fields α Normalization of action 31.2 The Gravitational Action 326 Einstein superfield Εμ α Component fields of Εμ D Lagrangian for Нџ □ Value of к О Total Lagrangian О Vacuum energy density D Minimum vacuum energy D De Sitter and anti-de Sitter spaces □ Why vacuum energy is negative ü Stability of flat space □ Weyl transformation 31.3 The Gravitino 333 Irreducibility conditions on gravitino field D Gravitino propagator G Gravitino kinematic Lagrangian □ Gravitino field equation □ Gravitino mass from broken supersymmetry Π Gravitino mass from s and ρ 31.4 Anomaly-Mediated Supersymmetry Breaking 337 First-order interaction with scale non-invariance superfield X D General formula for X О General first-order interaction □ Gaugino masses Π Gluino mass □ В parameter □ Wino and bino masses О A parameters 31.5 Local Supersymmetry Transformations 341 Wess-Zumino gauge for metric superfield Π Local supersymmetry transforma¬ tions □ Invariance of action xiv Contents 31.6 Supergravity to AH Orders 343 Local supersymmetry transformation of vierbein. gravitino, and auxiliary fields □ Extended spin connection □ Local supersymmetry transformation of general scalar supermultiplet D Product rules for general superfields ü Real matter superfields D Chiral matter superfields α Product rules for chiral superfields π Cosmological constant and gravitino mass α Lagrangian for supergravity and chiral fields with general Kahler potential and superpotential □ Elimination of auxiliary fields D Kahler metric о Weyl transformation π Scalar field potential D Conditions for flat space and unbroken supersymmetry О Complete bosonic Lagrangian π Canonical normalization α Combining superpotential and Kahler potential О No-scale models 31.7 Gravity-Mediated Supersymmetry Breaking 355 Early theories with hidden sectors □ Hidden sector gauge coupling strong at energy Λ Π First version: Observable and hidden sectors D Separable bare superpotential О General potential □ Terms of order к4Л8 « m4g □ Л estimated as « 1011 GeV Ο μ- and .Βμ -terms α Squark and slepton masses D Gaugino masses D ^-parameters D Second version: Observable, hidden, and modular sectors D Dynamically induced superpotential for modular superfields □ Effective superpotential of observable sector О μ -term О Potential of observable sector scalars О Terms of order к8Л12 » nŕg O Soft supersymmetry-breaking terms □ Л estimated as » 10° GeV D Shifts in modular fields D Absence of Су terms □ Squark and slepton masses D Gaugino masses Appendix The Vierbein Formalism 375 Problems 378 References 379 32 SUPERSYMMETRY ALGEBRAS IN HIGHER DIMENSIONS 382 32.1 General Supersymmetry Algebras 382 Classification of fermionic generators D Definition of weight D Fermionic gen¬ erators in fundamental spinor representation G Fermionic generators commute with Ρμ Q General form of anticommutation relations D Central charges G Anti¬ commutation relations for odd dimensionality G Anticommutation relations for even dimensionality Q .R-symmetry groups 32.2 Massless Multiplets 393 Little group O(d - 2) α Definition of spin j α Exclusion of j > 2 α Missing fermionic generators G Number of fermionic generators < 32 G N = 1 supersym¬ metry for d = U D Three-form massless particle Π Types ΠΑ, ΙΙΒ and heterotic supersymmetry for d = 10 32.3 p-Branes 397 New conserved tensors D Fermionic generators still in fundamental spinor repre- Contents xv sentation о Fermionic generators still commute with Ρμ D Symmetry conditions on tensor central charges □ 2-form and 5-form central charges for d = 11 Appendix Spinors in Higher Dimensions 401 Problems 407 References 407 AUTHOR INDEX 411 SUBJECT INDEX 416
adam_txt	Contents Sections marked with an asterisk are somewhat out of the book's main line of development and may be omitted in a first reading. PREFACE TO VOLUME III xvi NOTATION xx 24 HISTORICAL INTRODUCTION 1 24.1 Unconventional Symmetries and 'No-Go' Theorems 1 SU(6) symmetry Q Elementary no-go theorem for unconventional semi-simple compact Lie algebras Π Role of relativity 24.2 The Birth of Supersymmetry 4 Bosonic string theory α Fermionic coordinates D Worldsheet supersymmetry О Wess-Zumino model Π Precursors Appendix A S t/(6) Symmetry of Non-Relativistic Quark Models 8 Appendix В The Coleman-Mandula Theorem 12 Problems 22 References 22 25 SUPERSYMMETRY ALGEBRAS 25 25.1 Graded Lie Algebras and Graded Parameters 25 Fermionic and bosonic generators Π Super-Jacobi identity О Grassmann par¬ ameters G Structure constants from supergroup multiplication rules □ Complex conjugates 25.2 Supersymmetry Algebras 29 Haag-Lopuszanski-Sohnius theorem □ Lorentz transformation of fermionic gen¬ erators □ Central charges О Other bosonic symmetries D Я -symmetry D Simple vii viii Contents and extended supersymmetry D Four-component notation о Superconformai algebra 25.3 Space Inversion Properties of Supersymmetry Generators 40 Parity phases in simple supersymmetry □ Fermions have imaginary parity О Parity matrices in extended supersymmetry O Dirac notation 25.4 Massless Particle Supermultiplets 43 Known particles are massless for unbroken supersymmetry □ Helicity raising and lowering operators Q Simple supersymmetry doublets D Squarks, sleptons, and gauginos □ Gravitino Π Extended supersymmetry multiplets α Chirality problem for extended supersymmetry 25.5 Massive Particle Supermultiplets 48 Raising and lowering operators for spin 3-component О General massive multi¬ plets for simple supersymmetry D Collapsed supermultiplet D Mass bounds in extended supersymmetry О BPS states and short supermultiplets Problems 53 References 54 26 SUPERSYMMETRIC FIELD THEORIES 55 26.1 Direct Construction of Field Supermultiplets 55 Construction of simplest N = 1 field multiplet О Auxiliary field □ Infinitesi¬ mal supersymmetry transformation rules D Four-component notation ü Wess- Zumino supermultiplets regained 26.2 General Superfields 59 Superspace spinor coordinates О Supersymmetry generators as superspace dif¬ ferential operators π Supersymmetry transformations in superspace □ General superfields □ Multiplication rales □ Supersymmetric differential operators in su¬ perspace □ Supersymmetric actions for general superfields □ Parity of component fields □ Counting fermionic and bosonic components 26.3 Chiral and Linear Superfields 68 Chirality conditions on a general superfield D Left- and right-chiral superfields ü Coordinates χμ± D Differential constraints □ Product rules □ Supersymmetric &- terms α J^-terms equivalent to D-terms α Superpotentials G Kahler potentials ü Partial integration in superspace G Space inversion of chiral superfields □ .R-symmetry again D Linear superfields 26.4 Renormalizable Theories of Chiral Superfields 75 Counting powers о Kinematic Lagrangian D J^-term of the superpotential □ Complete Lagrangian D Elimination of auxiliary fields □ On-shell superalgebra π Vacuum solutions □ Masses and couplings □ Wess-Zumino Lagrangian regained Contents ix 26.5 Spontaneous Snpersymmetry Breaking in the Tree Approximation 83 O'Raifeartaigh mechanism □ R-symmetry constraints π Flat directions □ Gold- stino 26.6 Superspace Integrals, Field Equations, and the Current Superitela 86 Berezin integration D D- and J^-terms as superspace integrals G Potential su- perfields Π Superspace field equations π Conserved currents as components of linear superfields □ Conservation conditions in superspace 26.7 The Supercurrent 90 Supersymmetry current α Superspace transformations generated by the super- symmetry current □ Local supersymmetry transformations Π Construction of the supercurrent D Conservation of the supercurrent D Energy-momentum ten¬ sor and R-current Π Scale invariance and R conservation □ Non-uniqueness of supercurrent 26.8 General Kahler Potentials* 102 Non-renormalizable non-derivative actions □ D-term of Kahler potential □ Kahler metric О Lagrangian density □ Non-linear σ -models from spontaneous internal symmetry breaking □ Kahler manifolds □ Complexified coset spaces Appendix Majorana Spinors 107 Problems 111 References 112 27 SUPERSYMMETRIC GAUGE THEORIES 113 27.1 Gauge-Invariant Actions for Chiral Superfields 113 Gauge transformation of chiral superfields Π Gauge superfield V □ Extended gauge invariance □ Wess-Zumino gauge □ Supersymmetric gauge-invariant kine¬ matic terms for chiral superfields 27.2 Gauge-Invariant Action for Abelian Gauge Superfields 122 Field strength supermultiplet Π Kinematic Lagrangian density for Abelian gauge supermultiplet D Fayet-Iliopoulos terms о Abelian field-strength spinor super- field Wx □ Left- and right-chiral parts of Wx □ Wx as a superspace derivative of V □ Gauge invariance of W% □ 'Bianchi' identities in superspace 27.3 Gauge-Invariant Action for General Gauge Superfields 127 Kinematic Lagrangian density for non-Abelian gauge supermultiplet α Νοη- Abelian field-strength spinor superfield Wąx D Left- and right-chiral parts of □ 6-term D Complex coupling parameter τ ПА Renormalizable Gauge Theories with Chiral Superfields 132 Supersymmetric Lagrangian density □ Elimination of auxiliary fields О Condi¬ tions for unbroken supersymmetry О Counting independent conditions and field x Contents variables О Unitarity gauge Π Masses for spins 0, 1/2, and 1 □ Supersymmetry current О Non-Abelian gauge theories with general Kahler potentials □ Gaugino mass 27.5 Snpersymmetry Breaking in the Tree Approximation Resumed 144 Supersymmetry breaking in supersymmetric quantum electrodynamics □ General case: masses for spins 0, 1/2, and 1 □ Mass sum rule α Goldstino component of gaugino and chiral fermion fields 27.6 Perturbative Non-Renormalization Theorems 148 Non-renormalization of Wilsonian superpotential Π One-loop renormalization of terms quadratic in gauge superfields Π Proof using holomorphy and new symmetries with external superfields О Non-renormalization of Fayet-Iliopoulos constants ξά D For ξΛ = 0, supersymmetry breaking depends only on super- potential O Non-renormalizable theories 27.7 Soft Supersymmetry Breaking* 155 Limitation on supersymmetry-breaking radiative corrections D Quadratic diver¬ gences in tadpole graphs 27.8 Another Approach: Gauge-Invariant Supersymmetry Transformations 157 De Wit-Freedman transformation rules О Preserving Wess-Zumino gauge with combined supersymmetry and extended gauge transformations 27.9 Gauge Theories with Extended Supersymmetry* 160 N = 2 supersymmetry from N — 1 supersymmetry and .R-symmetry D La- grangian for N = 2 supersymmetric gauge theory D Eliminating auxiliary fields □ Supersymmetry currents □ Witten-Olive calculation of central charge O Non- renormalization of masses D BPS monopoles π Adding hypermultiplets G N = 4 supersymmetry Π Calculation of beta function D N = 4 theory is finite □ Montonen-Olive duality Problems 175 References 176 28 SUPERSYMMETRIC VERSIONS OF THE STANDARD MODEL 179 28.1 Superfields, Anomalies, and Conservation Laws 180 Quark, lepton, and gauge superfields D At least two scalar doublet superfields D J^-term Yukawa couplings D Constraints from anomalies □ Unsuppressed violation of baryon and lepton numbers D R-symmetry D R parity О /¿-term □ Hierarchy problem D Sparticle masses D Cosmological constraints on lightest superparticle 28.2 Supersymmetry and Strong-Electroweak Unification 188 Renormalization group equations for running gauge couplings □ Effect of super- Contents xi symmetry on beta functions □ Calculation of weak mixing angle and unification mass Π Just two scalar doublet superfields □ Coupling at unification scale 28.3 Where is Supersymmetry Broken? 192 Tree approximation supersymmetry breakdown ruled out D Hierarchy from non- perturbative effects of asymptotically free gauge couplings □ Gauge and grav¬ itational mediation of supersymmetry breaking α Estimates of supersymmetry- breaking scale Π Gravitino mass □ Cosmological constraints 28.4 The Minimal Supersymmetric Standard Model 198 Supersymmetry breaking by superrenormalizable terms □ General Lagrangian О Flavor changing processes □ Calculation of K° <-»· К □ Degenerate squarks and sleptons D CP violation D Calculation of quark chromoelectric dipole moment □ 'Naive dimensional analysis' □ Neutron electric dipole moment □ Constraints on masses and/or phases 28.5 The Sector of Zero Baryon and Lepton Number 209 D-term contribution to scalar potential D /¿-term contribution to scalar poten¬ tial □ Soft supersymmetry breaking terms □ Vacuum stability constraint on parameters α Finding a minimum of potential □ Βμ φ 0 Π Masses of CP-odd neutral scalars □ Masses of CP-even neutral scalars □ Masses of charged scalars D Bounds on masses □ Radiative corrections ü Conditions for electroweak symmetry breaking G Charginos and neutralinos D Lower bound on ΙμΙ 28.6 Gauge Mediation of Supersymmetry Breaking 220 Messenger superfields Q Supersymmetry breaking in gauge supermultiplet prop¬ agators D Gaugino masses □ Squark and slepton masses Π Derivation from holomorphy □ Radiative corrections о Numerical examples D Higgs scalar masses Π μ problem D Ац and Су parameters Π Gravitino as lightest sparticle О Next-to-lightest sparticle 28.7 Baryon and Lepton Non-Conservation 235 Dimensionality five interactions о Gaugino exchange О Gluino exchange sup¬ pressed D Wino and bino exchange effects Π Estimate of proton lifetime □ Favored modes of proton decay Problems 240 References 241 29 BEYOND PERTURBATION THEORY 248 29.1 General Aspects of Supersymmetry Breaking 248 Finite volume α Vacuum energy and supersymmetry breaking D Partially broken extended supersymmetry? □ Pairing of bosonic and fermionic states □ Pairing of vacuum and one-goldstino state O Witten index О Supersymmetry unbroken xii Contents in the Wess-Zumino model D Models with unbroken supersymmetry and zero Witten index D Large field values D Weighted Witten indices 29.2 Supersymmetry Current Sum Rules 256 Sum rale for vacuum energy density □ One-goldstino contribution □ The supersymmetry-breaking parameter F □ Soft goldstino amplitudes □ Sum rule for supersymmetry current-fermion spectral functions □ One-goldstino contribu¬ tion □ Vacuum energy density in terms of êF and D vacuum values D Vacuum energy sum rule for infinite volume 29.3 Non-Perturbative Corrections to the Superpotential 266 Non-perturbative effects break external field translation and R-conservation D Remaining symmetry О Example: generalized supersymmetric quantum chromo- dynamics Π Structure of induced superpotential for Ci > Сг О Stabilizing the vacuum with a bare superpotential □ Vacuum moduli in generalized supersym¬ metric quantum chromodynamics for Nc > Nf □ Induced superpotential is linear in bare superpotential parameters for Q = Сг □ One-loop renormalization of term for all Cu C2 29.4 Supersymmetry Breaking in Gauge Theories 276 Witten index vanishes in supersymmetric quantum electrodynamics D C-weighted Witten index О Supersymmetry unbroken in supersymmetric quantum electro¬ dynamics G Counting zero-energy gauge field states in supersymmetric quantum electrodynamics О Calculating Witten index for general supersymmetric pure gauge theories О Counting zero-energy gauge field states for general supersym¬ metric pure gauge theories α Weyl invariance D Supersymmetry unbroken in general supersymmetric pure gauge theories D Witten index and R anomalies Π Adding chiral scalars Π Model with spontaneously broken supersymmetry 29.5 The Seiberg-Witten Solution* 287 Underlying N = 2 supersymmetric Lagrangian □ Vacuum modulus Π Leading non-renormalizable terms in the eifective Lagrangian □ Effective Lagrangian for component fields Π Kahler potential and gauge coupling from a function й(Ф) □ S 1/(2) R-symmetry D Prepotential □ Duality transformation □ й(Ф) translation D Z<¡ R-symmetry D SL(2,Z)-symmetry D Central charge D Charge and magnetic monopole moments D Perturbative behavior for large \a\ □ Monodromy at infinity Π Singularities from dyons □ Monodromy at singularities Π Seiberg- Witten solution π Uniqueness proof Problems 3Q5 References 305 3β SUPERGRAPHS 307 ЗОЛ Potential Superfields ЗО8 Contents xiii Problem of chiral constraints □ Corresponding problem in quantum electro¬ dynamics D Path integrals over potential superfields 30.2 Superpr opagators 310 A troublesome invariance □ Change of variables □ Defining property of super- propagator □ Analogy with quantum electrodynamics ü Propagator for potential superfields О Propagator for chiral superfields 30.3 Calculations with Supergraphs 313 Superspace quantum effective action α Locality in fermionic coordinates α D- terms and J^-terms in effective action □ Counting superspace derivatives □ No renormalization of J^terms Problems 316 References 316 31 SUPERGRAVITY 318 31.1 The Metric Superfield 319 Vierbein formalism О Transformation of gravitational field □ Transformation of gravitino field Q Generalized transformation of metric superfield Ημ □ Interaction of Η џ with supercurrent Π Invariance of interaction □ Generalized transformation of Ημ components О Auxiliary fields □ Counting components Π Interaction of Ημ component fields α Normalization of action 31.2 The Gravitational Action 326 Einstein superfield Εμ α Component fields of Εμ D Lagrangian for Нџ □ Value of к О Total Lagrangian О Vacuum energy density D Minimum vacuum energy D De Sitter and anti-de Sitter spaces □ Why vacuum energy is negative ü Stability of flat space □ Weyl transformation 31.3 The Gravitino 333 Irreducibility conditions on gravitino field D Gravitino propagator G Gravitino kinematic Lagrangian □ Gravitino field equation □ Gravitino mass from broken supersymmetry Π Gravitino mass from s and ρ 31.4 Anomaly-Mediated Supersymmetry Breaking 337 First-order interaction with scale non-invariance superfield X D General formula for X О General first-order interaction □ Gaugino masses Π Gluino mass □ В parameter □ Wino and bino masses О A parameters 31.5 Local Supersymmetry Transformations 341 Wess-Zumino gauge for metric superfield Π Local supersymmetry transforma¬ tions □ Invariance of action xiv Contents 31.6 Supergravity to AH Orders 343 Local supersymmetry transformation of vierbein. gravitino, and auxiliary fields □ Extended spin connection □ Local supersymmetry transformation of general scalar supermultiplet D Product rules for general superfields ü Real matter superfields D Chiral matter superfields α Product rules for chiral superfields π Cosmological constant and gravitino mass α Lagrangian for supergravity and chiral fields with general Kahler potential and superpotential □ Elimination of auxiliary fields D Kahler metric о Weyl transformation π Scalar field potential D Conditions for flat space and unbroken supersymmetry О Complete bosonic Lagrangian π Canonical normalization α Combining superpotential and Kahler potential О No-scale models 31.7 Gravity-Mediated Supersymmetry Breaking 355 Early theories with hidden sectors □ Hidden sector gauge coupling strong at energy Λ Π First version: Observable and hidden sectors D Separable bare superpotential О General potential □ Terms of order к4Л8 « m4g □ Л estimated as « 1011 GeV Ο μ- and .Βμ -terms α Squark and slepton masses D Gaugino masses D ^-parameters D Second version: Observable, hidden, and modular sectors D Dynamically induced superpotential for modular superfields □ Effective superpotential of observable sector О μ -term О Potential of observable sector scalars О Terms of order к8Л12 » nŕg O Soft supersymmetry-breaking terms □ Л estimated as » 10° GeV D Shifts in modular fields D Absence of Су terms □ Squark and slepton masses D Gaugino masses Appendix The Vierbein Formalism 375 Problems 378 References 379 32 SUPERSYMMETRY ALGEBRAS IN HIGHER DIMENSIONS 382 32.1 General Supersymmetry Algebras 382 Classification of fermionic generators D Definition of weight D Fermionic gen¬ erators in fundamental spinor representation G Fermionic generators commute with Ρμ Q General form of anticommutation relations D Central charges G Anti¬ commutation relations for odd dimensionality G Anticommutation relations for even dimensionality Q .R-symmetry groups 32.2 Massless Multiplets 393 Little group O(d - 2) α Definition of 'spin' j α Exclusion of j > 2 α Missing fermionic generators G Number of fermionic generators < 32 G N = 1 supersym¬ metry for d = U D Three-form massless particle Π Types ΠΑ, ΙΙΒ and heterotic supersymmetry for d = 10 32.3 p-Branes 397 New conserved tensors D Fermionic generators still in fundamental spinor repre- Contents xv sentation о Fermionic generators still commute with Ρμ D Symmetry conditions on tensor central charges □ 2-form and 5-form central charges for d = 11 Appendix Spinors in Higher Dimensions 401 Problems 407 References 407 AUTHOR INDEX 411 SUBJECT INDEX 416
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author	Weinberg, Steven 1933-2021
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illustrated	Not Illustrated
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indexdate	2024-07-09T21:09:56Z
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isbn	0521670551 9780521670555
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spelling	Weinberg, Steven 1933-2021 Verfasser (DE-588)11562855X aut The quantum theory of fields 3 Supersymmetry Steven Weinberg Paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2005 XXII, 419 S. txt rdacontent n rdamedia nc rdacarrier Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s DE-604 (DE-604)BV010519919 3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016258146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Weinberg, Steven 1933-2021 The quantum theory of fields Quantenfeldtheorie (DE-588)4047984-5 gnd
subject_GND	(DE-588)4047984-5
title	The quantum theory of fields
title_auth	The quantum theory of fields
title_exact_search	The quantum theory of fields
title_exact_search_txtP	The quantum theory of fields
title_full	The quantum theory of fields 3 Supersymmetry Steven Weinberg
title_fullStr	The quantum theory of fields 3 Supersymmetry Steven Weinberg
title_full_unstemmed	The quantum theory of fields 3 Supersymmetry Steven Weinberg
title_short	The quantum theory of fields
title_sort	the quantum theory of fields supersymmetry
topic	Quantenfeldtheorie (DE-588)4047984-5 gnd
topic_facet	Quantenfeldtheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016258146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV010519919
work_keys_str_mv	AT weinbergsteven thequantumtheoryoffields3

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