Supergravity : from first principles to modern applications / / Gianguido Dall'Agata, Marco Zagermann

• Autore: Dall'Agata Gianguido
• Pubblicazione: Berlin, Germany : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (301 pages)
• Disciplina: 530.142
• Soggetto topico: Supergravity
• Persona (resp. second.): ZagermannMarco
• Nota di contenuto: Intro -- Preface -- Acknowledgements -- Contents -- Part I Foundations and Pure Supergravity -- 1 Introduction -- 1.1 The Many Facets of Supergravity -- 1.2 Plan of the Lectures -- 1.3 A Quick Guide Through Our Spinor Conventions -- 1.3.1 Two-Component Spinors -- 1.3.2 Four-Component Spinors -- 1.3.2.1 Dirac Spinors -- 1.3.2.2 The Weyl Condition -- 1.3.2.3 The Majorana Condition -- 1.3.3 Susy Algebra in Four Dimensions -- Exercises -- References -- 2 From Global to Local Supersymmetry -- 2.1 Promoting Supersymmetry to a Local Symmetry -- 2.2 The Gravitino -- 2.2.1 The Gravitino Action -- 2.2.2 The Gravitino Multiplet -- Exercises -- References -- 3 Gravity and Spinors -- 3.1 The Standard Metric Formulation -- 3.2 The Vielbein Basis and Cartan's Formalism -- 3.3 Spinors in Curved Spacetime -- Exercises -- 4 Pure N = 1 Supergravity in Four Dimensions -- 4.1 Pure Supergravity: The Action and SUSY Rules -- 4.1.1 Second-Order Formalism -- 4.1.2 First-Order Formalism -- 4.1.3 1.5-Order Formalism -- 4.2 Adding a Cosmological Constant -- 4.2.1 Construction of the Action -- 4.2.2 Mass in AdS -- 4.A Appendix: Gauging the Poincaré Algebra -- 4.A.1 Gauging the Super Poincaré Algebra -- Exercises -- References -- Part II Matter Couplings and Phenomenology -- 5 Matter Couplings in Global Supersymmetry -- 5.1 Our Approach -- 5.2 Chiral Multiplets in Global Supersymmetry -- 5.2.1 The Renormalizable Wess-Zumino Model -- 5.2.2 Non-linear Sigma Models I: The Holonomy Group -- 5.2.2.1 The Holonomy Group of the Scalar Manifold -- 5.2.3 Non-linear Sigma Models II: Fermions and Supersymmetry -- 5.2.4 4D Supersymmetry and Kähler Manifolds -- 5.3 Globally Supersymmetric Gauge Theories -- 5.3.1 Super Maxwell Theory -- 5.3.2 Super Yang-Mills Theory -- 5.3.3 Coupling Super Maxwell/Yang-Mills Theories to Chiral Multiplets. ; 5.3.4 Non-minimal Kinetic Terms for Vector Multiplets: The Gauge Kinetic Function -- 5.3.5 Non-linear σ-Models III: Global and Local Symmetries -- 5.3.6 Killing Prepotentials, D-Terms, and the General Globally Supersymmetric Lagrangian -- 5.3.6.1 Proof of the Equivariance Condition -- 5.3.6.2 Two Examples of Gaugings with Fayet-Iliopoulos Constants -- 5.3.6.3 Lagrangian and Susy Rules -- 5.3.6.4 A Familiar Special Case: Canonical Kähler Potential and Minimal Gauge Kinetic Function -- 5.4 Supersymmetry Breaking -- Exercises -- References -- 6 Matter Couplings in Supergravity -- 6.1 New Supergravity Couplings -- 6.1.1 Coupling Chiral Multiplets to Supergravity -- 6.1.2 The Kähler Covariant Derivative -- 6.1.3 Additional Bare Superpotential Terms -- 6.1.4 Inclusion of Vector Multiplets -- 6.1.5 More on D-Terms -- 6.1.6 The Gradient Flow Relations -- 6.1.7 Final Remarks -- 6.2 Kähler-Hodge Manifolds -- 6.2.1 An Example: Quantization of Newton's Constant -- Exercises -- References -- 7 Phenomenological Aspects -- 7.1 Spontaneous Supersymmetry Breaking -- 7.1.1 Vacua -- 7.1.2 General Features of Spontaneous Supersymmetry Breaking -- 7.1.3 Mass Scales Related to Supersymmetry Breaking -- 7.1.3.1 The Supersymmetry Breaking Scale Msusy -- 7.1.3.2 The Vacuum Energy Scale Mvac -- 7.1.3.3 The Gravitino Mass M3/2 -- 7.1.3.4 The Soft Masses Msoft -- 7.1.3.5 Moduli Masses Mmod -- 7.1.3.6 The Inflationary Energy Scale Minf -- 7.1.4 Rigid Limits -- 7.2 Gravitino, Goldstino, and Super-Higgs Mechanism -- 7.2.1 The Goldstino in Global Supersymmetry -- 7.2.2 The Goldstino and the Gravitino in Supergravity -- 7.2.3 Gravitino Couplings -- 7.2.4 Generalizations -- 7.3 Mass Sum Rules and Mediation Mechanisms -- 7.3.1 Mass Sum Rules, Hidden Sectors, and Mediation Mechanisms -- 7.3.2 Gravity-Mediated Supersymmetry Breaking and the Polonyi Model -- 7.3.2.1 The Polonyi Model. ; 7.3.2.2 Illustration of Gravity Mediation: Scalar Soft Terms -- 7.3.2.3 Gaugino Masses -- 7.4 Moduli Stabilization, de Sitter Vacua, and Inflation -- 7.4.1 Moduli Stabilization and Moduli Masses -- 7.4.1.1 The sgoldstini -- 7.4.1.2 A Constraint on the Lightest Modulus Mass -- 7.4.1.3 Possible Caveats -- 7.4.1.4 A Counterexample with Large Curvature -- 7.4.2 No Scale Models -- 7.4.2.1 The Simplest Example -- 7.4.2.2 Generalizations -- 7.4.2.3 Adding Scalars Without No-Scale Property -- 7.4.2.4 A D-Term Analogue -- 7.4.3 Dark Energy and de Sitter Vacua -- 7.4.4 Inflation and the Supergravity η-Problem -- 7.A Appendix: Proof of Eq.(7.114) -- Exercises -- References -- Part III Extended, Gauged and Higher-Dimensional Supergravity -- 8 Extended Supergravities -- 8.1 Electric-Magnetic Duality -- 8.2 N=2 Supergravity -- 8.2.1 N=2 Vector Multiplets and Special Kähler Geometry -- 8.2.1.1 Rigid (``Affine'') Special Kähler Geometry -- 8.2.1.2 Local (``Projective'') Special Kähler Geometry -- 8.2.2 N=2 Hypermultiplets and Hyper-Kähler vs. Quaternionic Kähler Geometry -- 8.3 Extended Supergravity with N≥3 -- 8.A Appendix: Details on and Origin of Local Special Kähler Geometry -- 8.A.1 The Symplectic Section and Its KählerTransformation -- 8.A.2 The Kähler Potential -- 8.A.3 The Existence of a Prepotential -- 8.A.4 The Gauge Kinetic Matrix -- 8.B Appendix: Quaternionic-Kähler vs. Hyper-Kähler Manifolds of Hypermultiplets -- 8.B.1 Sp(nH)SU(2)-Adapted Vielbein -- 8.B.2 Holonomy and Curvature -- Exercises -- References -- 9 Gauged Supergravity -- 9.1 Supergravities and Scalar Potentials -- 9.2 Duality -- 9.2.1 From Electric-Magnetic Duality to U-Duality -- 9.3 Gauging and Symplectic Frames -- 9.4 Coset Manifolds and Gauging -- 9.4.1 Vielbein, Metric, and Isometries of G/H -- 9.4.2 The Special-Kähler Manifold SU(1,1)/U(1) and Inequivalent Symplectic Frames. ; 9.5 Gauging and the Embedding Tensor -- 9.5.1 Constraints on the Embedding Tensor -- 9.5.2 Couplings -- 9.5.3 An Example: The Maximal Theory -- 9.6 Classifying Gaugings -- 9.6.1 The Quotient Space S -- 9.6.2 The S Space of SO(8) Maximal Gauged Supergravity -- References -- 10 Supergravity in Arbitrary Dimensions -- 10.1 Higher-Dimensional Theories -- 10.2 Example: D=11 Supergravity -- 10.3 Dimensional Reduction and Ten-Dimensional Supergravities -- 10.4 Dimensional Reduction and the Origin of Gauged Supergravities -- 10.5 Example: D=5 -- 10.5.1 N=2 in 5D -- 10.5.1.1 The Geometry of MV -- 10.5.1.2 The Geometry of MH -- 10.5.2 N=4 in 5D -- 10.5.3 N=6 in 5D -- 10.5.4 N=8 in 5D -- 10.5.5 Gaugings and Tensor Fields -- 10.A Appendix: Clifford Algebras and Spinors in Arbitrary D -- 10.A.1 Irreducible Representations of Cliff(1,D-1) -- 10.A.1.1 Even Dimensions -- 10.A.1.2 Odd Dimensions -- 10.A.2 Irreducible Spinor Representations of SO0(1,D-1) -- 10.A.2.1 Chirality Conditions -- 10.A.2.2 Reality Conditions -- 10.A.3 Majorana and Weyl Condition -- Exercises -- References -- Index.
• Titolo autorizzato: Supergravity
• ISBN: 3-662-63980-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466843403316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture notes in physics ; ; Volume 991.