Introduction to Supergravity and its Applications

Horațiu Năstase is a researcher at the Institute for Theoretical Physics, State University of São Paulo. He completed his Ph.D. at Stony Brook with Peter van Nieuwenhuizen, co-discoverer of supergravity. While in Princeton as a postdoc, in a 2002 paper with David Berenstein and Juan Maldacena, he started the pp-wave correspondence, a sub-area of the AdS/CFT correspondence. He has written more than 100 scientific articles and 6 other books: Introduction to the AdS/CFT Correspondence (2015), String Theory Methods for Condensed Matter Physics (2017), Classical Field Theory (2019), Introduction to Quantum Field Theory (2019), Cosmology and String Theory (2019) and Quantum Mechanics: A Graduate Course (2022).

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.