Introduction to Supergravity and its Applications

Suitable for a focused first course, this text gives Ph.D. students the necessary tools to do research that uses supergravity.

Horatiu Nastase (Author)

9781009445597, Cambridge University Press

Hardback, published 21 November 2024

444 pages
26.2 x 18.5 x 3 cm, 0.97 kg

This graduate textbook covers the basic formalism of supergravity, as well as its modern applications, suitable for a focused first course. Assuming a working knowledge of quantum field theory, Part I gives the basic formalism, including on- and off-shell supergravity, the covariant formulation, superspace and coset formulations, coupling to matter, higher dimensions and extended supersymmetry. A wide range of modern applications are introduced in Part II, including string theoretical (T- and U-duality, AdS/CFT, susy and sugra on the worldsheet, superembeddings), gravitational (p-brane solutions and their susy, attractor mechanism, Witten's positive energy theorem) and phenomenological (inflation in supergravity, supergravity no-go theorems, string theory constructions at low energies, minimal supergravity and its susy-breaking). The broader emphasis on applications than competing texts gives Ph.D. students the tools they need to do research that uses supergravity and benefits researchers already working in areas related to supergravity.

1. Introduction to general relativity 1: kinematics and Einstein equations
2. Introduction to general relativity 2: Vielbein and spin connection, anti-de Sitter space, black holes
3. Introduction to supersymmetry 1: Wess–Zumino models, onshell and off-shell supersymmetry
4. Introduction to supersymmetry 2: multiplets and extended supersymmetry
5. Introduction to supersymmetry 3: superspace formalism in d = 4. Perturbative susy breaking
6. 4-dimensional on-shell supergravity and how to count degrees of freedom
7. 3-dimensional N = 1 off-shell supergravity
8. Coset theory and rigid superspace
9. Covariant formulation of YM in rigid superspace and local superspace formalisms
10. N = 1 4-dimensional off-shell supergravity
11. N = 1 4-dimensional supergravity in superspace
12. Superspace actions and coupling supergravity with matter
13. Kaluza–Klein (KK) dimensional reduction and examples
14. Spherical harmonics and the KK expansion on sphere, coset and group spaces
15. N = 2 sugra in 4 dimensions, general sugra theories and N = 1 sugra in 11 dimensions
16. AdS4 × S7 nonlinear KK compactification of 11-dimensional supergravity and related notions
17. (Abelian and non-Abelian) T-dualities and other solution-generating techniques: TsT, O(d, d), 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 attractor mechanism, 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. Towards realistic embeddings of the Standard Model using supergravity
31. Minimal sugra, phenomenology and models of susy breaking
References
Index.

Subject Areas: Statistical physics [PHS]