Verfügbarkeit: The quantum theory of fields

The quantum theory of fields: 3 Supersymmetry

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Bibliographische Detailangaben
1. Verfasser:	Weinberg, Steven 1933-2021 (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2010
Ausgabe:	3rd pr.
Schlagworte:	Quantenfeldtheorie
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Beschreibung:	XXII, 419 S.
ISBN:	0521670551 9780521670555

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Datensatz im Suchindex

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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 HI xvi NOTATION xx 24 HISTORICAL INTRODUCTION 1 24.1 Unconventional Symmetries and No-Go Theorems 1 S (7(6) symmetry D Elementary no-go theorem for unconventional semi-simple compact Lie algebras D Role of relativity 242 The Birth of Supersymmetry 4 Bosonic string theory D Fermionic coordinates □ Woridsheet supersymmetry о Wess-Zumino model О Precursors Appendix A S Щ6) Symmetry of Non-RelatWistic Quark Modeb 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 □ Super-Jacobi identity Π Grassmann par¬ ameters D Structure constants from supergroup multiplication rules О Complex conjugates 25.2 Supersymmetry Algebras 29 Haag-Lopuszanski-Sohnius theorem O Lorentz transformation of fermionic gen¬ erators □ Central charges D Other bosonic symmetries D Ä-symmetry D Simple vii viii Contents and extended supersymmetry □ Four-component notation ü Superconformal algebra 253 Space Inversion Properties of Supersymmetry Generators 40 Parity phases in simple supersymmetry D Fermions have imaginary parity □ Parity matrices in extended supersymmetry D Dirac notation 25.4 Masskss Particle Supermultiplets 43 Known particles are massless for unbroken supersymmetry O Helicity raising and lowering operators о Simple supersymmetry doublets O Squarks, sleptons, and gauginos □ Gravitino О Extended supersymmetry multiplets О Chirality problem for extended supersymmetry 253 Massive Particle Supermahiplets 48 Raising and lowering operators for spin 3-component O General massive multi¬ plets for simple supersymmetry □ Collapsed supermultiplet О Mass bounds in extended supersymmetry о BPS states and short supermultiplets Problems S3 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 о Infinitesi¬ mal supersymmetry transformation rules о Four-component notation D Wess- Zumino supermultiplets regained 26.2 General Superfields 59 Superspace spinor coordinates D Supersymmetry generators as superspace dif¬ ferential operators □ Supersymmetry transformations in superspace О General superfields □ Multiplication rules D Supersymmetric differential operators in su¬ perspace Π Supersymmetric actions for general superfields □ Parity of component fields о Counting fermionic and bosonic components 263 Chiral and Linear Superfields 68 Chirality conditions on a general superfield D Left- and right-chiral superfields α Coordinates xf± О Differential constraints D Product rules D Supersymmetric &- terms D ^-terms equivalent to D-terms D Superpotentials о Kahler potentials D Partial integration in superspace D Space inversion of chiral superfields α R-symmetry again □ Linear superfields 26.4 Renonnalizable Theories of Chiral Superfields 75 Counting powers α Kinematic Lagrangian D ^-term of the superpotential O Complete Lagrangian D Elimination of auxiliary fields α On-shell superalgebra о Vacuum solutions о Masses and couplings D Wess-Zumino Lagrangian regained Contents ix 263 Spontaneous Supersymmetry Breaking in the Tree Approximation 83 O Raifeartaigh mechanism ü R-symmetry constraints Π Flat directions D Gold¬ stino 26.6 Superspace Integrals, Field Equations, and the Current Superfield 86 Berezin integration D D- and ^-terms as superspace integrals D Potential su- perfields ü Superspace field equations □ Conserved currents as components of linear superfields □ Conservation conditions in superspace 26.7 The Supercurrent 90 Supersymmetry current ü Superspace transformations generated by the super- symmetry current □ Local supersymmetry transformations ü Construction of the supercurrent о Conservation of the supercurrent □ Energy-momentum ten¬ sor and R-current □ Scale invariance and R conservation □ Non-uniqueness of supercurrent 26.8 General Kahler Potentials* 102 Non-renormalizable non-derivative actions α ß-term of Kahler potential ü Kahler metric ü Lagrangian density o Non-linear σ -models from spontaneous internal symmetry breaking α Kahler manifolds ü Complexified coset spaces Appendix Majorana Spinors 107 Problems 111 References 112 27 SUPERSYMMETRIC GAUGE THEORIES 113 27.1 Gauge-Invariant Actions for Cbiral Superfields 113 Gauge transformation of chiral superfields □ Gauge superfield V □ Extended gauge invariance О Wess-Zumino gauge O Supersymmetric gauge-invariant kine¬ matic terms for chiral superfields 27.2 Gauge-Invariant Action for Abelian Gauge Superfields 122 Field strength supermultiplet D Kinematic Lagrangian density for Abelian gauge supermultiplet □ Fayet-Iliopoulos terms D Abelian field-strength spinor super¬ field Wa О Left- and right-chiral parts of W^ □ Wa as a superspace derivative of V o Gauge invariance of Wa O Bianchi identities in superspace 273 Gauge-Invariant Action for General Gauge Superfields 127 Kinematic Lagrangian density for non-Abelian gauge supermultiplet Π Νοη- Abelian field-strength spinor superfield WAaL □ Left- and right-chiral parts of W a,, О 0-term Π Complex coupling parameter τ 27.4 Renormalizable Gauge Theories with Chiral Superfields 132 Supersymmetric Lagrangian density О Elimination of auxiliary fields Π Condi¬ tions for unbroken supersymmetry О Counting independent conditions and field χ Contents variables D Unitarity gauge □ Masses for spins 0, 1/2, and 1 □ Supersymmetry current Π Non-Abelian gauge theories with general Kahler potentials О Gaugino mass 27.5 Sepersymroetry Breaking in the Tree Approximation Resumed 144 Supersymmetry breaking in supersymmetric quantum electrodynamics D General case: masses for spins 0,1/2, and 1 α Mass sum rule Π Goldstino component of gaugino and chiral fermion fields 27.6 Perturbarhe Non-Renormalizatíon Theorems 148 Non-renormalization of Wilsonian superpotential □ One-loop renormalization of terms quadratic in gauge superfields π Proof using holomorphy and new symmetries with external superfields Ρ Non-renormalization of Fayet-Iliopoulos constants ξ,Λ □ For ϊ,α = 0, supersymmetry breaking depends only on super- potential O Non-renormalizable theories 27.7 Soft Supersymmetry Breaking* 155 Limitation on supersymmetry-breaking radiative corrections О Quadratic diver¬ gences in tadpole graphs 27.8 Another Approach: Gauge-Invariant Supersymmetry Transformations 157 De Wit-Freedman transformation rules α Preserving Wess-Zumino gauge with combined supersymmetry and extended gauge transformations 27 J Gange 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 G Supersymmetry currents О Witten-Olive calculation of central charge G Non- renormalization of masses D BPS monopoles □ Adding hypermultiplets D N = 4 supersymmetry D Calculation of beta function O N = 4 theory is finite D Montonen-Olive duality ProHeins 175 References 176 28 SUPERSYMMETRIC VERSIONS OF THE STANDARD MODEL 179 28.1 Superfields, Anomalies, and Conservation Laws 180 Quark, lepton, and gauge superfields Π At least two scalar doublet superfields D .F-term Yukawa couplings ü Constraints from anomalies D Unsuppressed violation of baryon and lepton numbers D Ä-symmetry D R parity □ μ -term D Hierarchy problem O Sparticle masses O Cosmological constraints on lightest superparticle 28.2 Supersymmetry and Strong-Electroweak Unification 188 Renormalization group equations for running gauge couplings D Effect of super- Contents xi symmetry on beta functions G Calculation of weak mixing angle and unification mass D Just two scalar doublet superfields D Coupling at unification scale 283 Where is Supersymmetry Broken? 192 Tree approximation supersymmetry breakdown ruled out Q Hierarchy from non- perturbative effects of asymptotically free gauge couplings D Gauge and grav¬ itational mediation of supersymmetry breaking □ Estimates of supersymmetry- breaking scale G Gravitino mass G Cosmological constraints 28.4 The Minimal Supersymmetric Standard Model 198 Supersymmetry breaking by superrenormalizable terms G General Lagrangian G Flavor changing processes □ Calculation of K° - K G Degenerate squarks and sleptons G CP violation G Calculation of quark chromoelectric dipole moment G Naive dimensional analysis α Neutron electric dipole moment G Constraints on masses and/or phases 28.5 The Sector of Zero Baryon and Lepton Number 209 D-term contribution to scalar potential G μ -term contribution to scalar poten¬ tial G Soft supersymmetry breaking terms G Vacuum stability constraint on parameters G Finding a minimum of potential Ο Β μ φ 0 G Masses of CP-odd neutral scalars G Masses of CP-even neutral scalars G Masses of charged scalars α Bounds on masses G Radiative corrections α Conditions for electroweak symmetry breaking G Charginos and neutralinos G Lower bound on \|μ\| 28.6 Gauge Mediation of Supersymmetry Breaking 220 Messenger superfields α Supersymmetry breaking in gauge supermultiplet prop¬ agators О Gaugino masses О Squark and slepton masses G Derivation from holomorphy G Radiative corrections G Numerical examples G Higgs scalar masses G μ problem O A¡¡ and C¡¡ parameters G Gravitino as lightest sparitele G Next-to-lightest spaniele 28.7 Baryon and Lepton Non-Conservation 235 Dimensionality five interactions G Gaugino exchange G Gluino exchange sup¬ pressed G Wino and bino exchange effects G Estimate of proton lifetime G Favored modes of proton decay Problems 240 References 241 29 BEYOND PERTURBATION THEORY 248 29.1 General Aspects of Supersymmetry Breaking 248 Finite volume G Vacuum energy and supersymmetry breaking G Partially broken extended supersymmetry? G Pairing of bosonic and fermionic states G Pairing of vacuum and one-goldstino state □ Witten index G Supersymmetry unbroken xii Contents in the Wess-Zumino model D Models with unbroken supersymmetry and zero Witten index α Large field values α Weighted Witten indices 792 Supersymmetry Current Sum Rules 256 Sum rule for vacuum energy density □ One-goldstino contribution Q The supersymmetry-breaking parameter F □ Soft goldstino amplitudes О Sum rule for supersymmetry current-fermion spectral functions □ One-goldstino contribu¬ tion D Vacuum energy density in terms of SF and D vacuum values О Vacuum energy sum rule for infinite volume 293 Noo-Perrorbative Corrections to the Superpotential 266 Non-perturbative effects break external field translation and R-conservation D Remaining symmetry □ Example: generalized supersymmetric quantum chromo- dynamics О Structure of induced superpotential for C > Сг D Stabilizing the vacuum with a bare superpotential O Vacuum moduli in generalized supersym¬ metric quantum chromodynamics for Nc > Nf □ Induced superpotential is linear in bare superpotential parameters for C = Сг О One-loop renormalization of [W.WJjr term for all Cu C2 29.4 Supersymmetry Breaking in Gauge Theories 276 Witten index vanishes in supersymmetric quantum electrodynamics O C-weighted Witten index Q Supersymmetry unbroken in supersymmetric quantum electro¬ dynamics D 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 Q Weyl invariance □ Supersymmetry unbroken in general supersymmetric pure gauge theories O Witten index and R anomalies Q Adding chiral scalars О Model with spontaneously broken supersymmetry 29.5 The Seiberg-Wirten Solution* 287 Underlying N = 2 supersymmetric Lagrangian D Vacuum modulus □ Leading non-renormalizable terms in the effective Lagrangian □ Effective Lagrangian for component fields О Kahler potential and gauge coupling from a function Л(Ф) α SU(2) R-symmetry Q Prepotential G Duality transformation α Я(Ф) translation G üg R-symmetry G ЅЦ2, Z)-symmetry G Central charge G Charge and magnetic monopole moments D Perturbative behavior for large a G Monodramy at infinity D Singularities from dyons G Monodramy at singularities α Seiberg- Witten solution G Uniqueness proof Problems 305 References 305 30 SUPERGRAPHS 307 30.1 Potential Superfiekk 308 Contents xiii Problem of chiral constraints □ Corresponding problem in quantum electro¬ dynamics D Path integrals over potential superfields 30.2 Superpropagators 310 A troublesome invariance □ Change of variables D Defining property of super- propagator □ Analogy with quantum electrodynamics □ Propagator for potential superfields G Propagator for chiral superfields 303 Calculations with Supergraphs 313 Superspace quantum effective action □ Locality in fermionic coordinates α D- terms and ^ -terms in effective action □ Counting superspace derivatives D No renormalization of ^ -terms Problems 316 References 316 31 SUPERGRAVITY 318 31.1 The Metric Superfield 319 Vierbein formalism □ Transformation of gravitational field G Transformation of gravitino field α Generalized transformation of metric superfield Ημ G Interaction of Ημ with supercurrent G Invariance of interaction Q Generalized transformation of Ημ components G Auxiliary fields G Counting components G Interaction of Ημ component fields G Normalization of action 31.2 The Gravitational Action 326 Einstein superfield Εμ α Component fields of Εμ G Lagrangian for Ημ G Value of к G Total Lagrangian G Vacuum energy density G Minimum vacuum energy G De Sitter and anti-de Sitter spaces G Why vacuum energy is negative G Stability of flat space α Weyl transformation 313 The Gravitino 333 Irreducibility conditions on gravitino field G Gravitino propagator G Gravitino kinematic Lagrangian G Gravitino field equation G Gravitino mass from broken supersymmetry Q Gravitino mass from s and p 31.4 Anomaly-Mediated Supersymmetry Breaking 337 First-order interaction with scale non-invariance superfield X G General formula for X G General first-order interaction G Gaugino masses G Gluino mass G B parameter G Wino and bino masses G A parameters 313 Local Supersymmetry Transformations 341 Wess-Zumino gauge for metric superfield G Local supersymmetry transforma¬ tions G Invariance of action xiv Contents 31.6 Supergravity to АО Orders 343 Local supersymmetry transformation of vierbein, gravitino, and auxiliary fields D Extended spin connection ö Local supersymmetry transformation of general scalar supermultiplet D Product rules for general superfields D Real matter superfields О Chiral matter superfields □ Product rules for chiral superfields D Cosmological constant and gravitino mass о Lagrangian for supergravity and chiral fields with general Kahler potential and superpotential D Elimination of auxiliary fields О Kahler metric □ Weyl transformation D Scalar field potential О Conditions for flat space and unbroken supersymmetry □ Complete bosonic Lagrangian D Canonical normalization D Combining superpotential and Kahler potential О No-scale models 31.7 Gravity-Mediated Supersymmetry Breaking 355 Early theories with hidden sectors D Hidden sector gauge coupling strong at energy Л D First version: Observable and hidden sectors О Separable bare superpotential D General potential О Terms of order к4Л8 » m* О Л estimated as * IO GeV D μ- and Βμ -terms α Squark and slepton masses O Gaugino masses D ^-parameters D Second version: Observable, hidden, and modular sectors О 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 » nt* О Soft supersymmetry-breaking terms о Л estimated as « 1013 GeV α Shifts in modular fields π Absence of C¡j terms α Squark and slepton masses □ Gaugino masses Appendix Tbe Vierbein Formalism 375 Problems 378 References 379 32 SUPERSYMMETRY ALGEBRAS IN HIGHER DIMENSIONS 382 32.1 General Supersymmetry Algebras 382 Classification of fermionic generators α Definition of weight D Fermionic gen¬ erators in fundamental spinor representation D Fermionic generators commute with Ρμ D General form of anticommutation relations D Central charges □ Anti- commutation relations for odd dimensionality α Anticommutation relations for even dimensionality D /{-symmetry groups 312 Masskss Multiplets 393 Little group O(d - 2) α Definition of spin ; α Exclusion of j > 2 Π Missing fermionic generators О Number of fermionic generators <, 32 Ο Ν — 1 supersym¬ metry for d = 11 О Three-form massless particle D Types IIA, IIB and heterotic supersymmetry for d = 10 323 p-Branes 397 New conserved tensors □ Fermionic generators still in fundamental spinor repre- Contents xv sentation D Fermionic generators still commute with Ρμ □ Symmetry conditions on tensor central charges О 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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spelling	Weinberg, Steven 1933-2021 Verfasser (DE-588)11562855X aut The quantum theory of fields 3 Supersymmetry Steven Weinberg 3rd pr. Cambridge [u.a.] Cambridge Univ. Press 2010 XXII, 419 S. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke 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=020776945&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_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=020776945&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT weinbergsteven thequantumtheoryoffields3

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