Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Introduction
- Part I Formalism
- Part II Applications
- 16 AdS7 × S4 nonlinear KK compactification of 11-dimensional supergravity and related notions
- 17 (Abelian and nonabelian) T-dualities and other solution generatingtechniques: TsT, O(d, d), and null Melvin twist
- 18 Extremal and black p-brane solutions of supergravity; Tseytlin’s harmonic function rule
- 19 Supersymmetry of solutions, classification via susy algebra, intersecting brane solutions
- 20 U-duality group acting on supergravity theories and on solutions,M theory unification
- 21 Gravity duals: Decoupling limit and Penrose limits on solutions and algebras
- 22 Supersymmetric AdS/CFT gravity dual pairs and their deformations (susy, marginal, integrable)
- 23 Extremal black holes, the attractormechanism, and holography
- 24 Supersymmetric string (NS-R, GS, Berkovits) and supergravity on the worldsheet vs. spacetime supergravity
- 25 Kappa symmetry and spacetime supergravity equations of motion; superembedding formalism
- 26 Supergravity and cosmological inflation models
- 27 Maldacena–Núñez and supergravity no-go theorems; loopholes
- 28 Witten’s positive energy theorem in general relativity and connection with supergravity
- 29 Compactification of low-energy string theory
- 30 Toward realistic embeddings of the Standard Model using supergravity
- 31 Minimal sugra, phenomenology, andmodels of susy breaking
- References
- Index
16 - AdS7 × S4 nonlinear KK compactification of 11-dimensional supergravity and related notions
from Part II - Applications
Published online by Cambridge University Press: 14 November 2024
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Introduction
- Part I Formalism
- Part II Applications
- 16 AdS7 × S4 nonlinear KK compactification of 11-dimensional supergravity and related notions
- 17 (Abelian and nonabelian) T-dualities and other solution generatingtechniques: TsT, O(d, d), and null Melvin twist
- 18 Extremal and black p-brane solutions of supergravity; Tseytlin’s harmonic function rule
- 19 Supersymmetry of solutions, classification via susy algebra, intersecting brane solutions
- 20 U-duality group acting on supergravity theories and on solutions,M theory unification
- 21 Gravity duals: Decoupling limit and Penrose limits on solutions and algebras
- 22 Supersymmetric AdS/CFT gravity dual pairs and their deformations (susy, marginal, integrable)
- 23 Extremal black holes, the attractormechanism, and holography
- 24 Supersymmetric string (NS-R, GS, Berkovits) and supergravity on the worldsheet vs. spacetime supergravity
- 25 Kappa symmetry and spacetime supergravity equations of motion; superembedding formalism
- 26 Supergravity and cosmological inflation models
- 27 Maldacena–Núñez and supergravity no-go theorems; loopholes
- 28 Witten’s positive energy theorem in general relativity and connection with supergravity
- 29 Compactification of low-energy string theory
- 30 Toward realistic embeddings of the Standard Model using supergravity
- 31 Minimal sugra, phenomenology, andmodels of susy breaking
- References
- Index
Summary
From the unique N = 1 11-dimensional supergravity, all the other supergravities in lower dimensions are thought to be obtained. To obtain the seven-dimensional gauged supergravity, we first describe a first-order formulation of 11-dimensional supergravity. Then, we describe a nonlinear ansatz, leading to a consistent truncation. The concepts of consistent truncation and nonlinear ansatze are described, and the linearized ansatz on S4 and the spherical harmonics on S4 are reviewed. Relatedly, we describe the Lagrangians and transformation rules for the (maximal) N = 8 d = 4, N = 8 d = 5, and N = 4 d = 7 gauged supergravities, the massive type IIA 10-dimensional supergravity, type IIB 10-dimensional supergravity, and some general properties of gaugings, in particular the non-compact ISO(7) gauging. We end with modified supergravities: the one with SO(1, 3) × SU(8) local Lorentz covariance in 11 dimensions, the generalization known as exceptional field theory, and the geometric approach to supergravity, in particular d'Auria and Fré’s 11-dimensional supergravity with OSp(1|32) invariance.
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- Introduction to Supergravity and its Applications , pp. 177 - 209Publisher: Cambridge University PressPrint publication year: 2024