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.
This graduate textbook covers the basic formalism of supergravity, as well as a wide range of its modern applications, suitable for a focused first course. Assuming a working knowledge of quantum field theory, it gives Ph.D. students the tools they need to do research that uses supergravity.
Daugiau informacijos
Suitable for a focused first course, this text gives Ph.D. students the necessary tools to do research that uses 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: WessZumino 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. KaluzaKlein
(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. MaldacenaNśńez 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.
Horaiu Nstase is a researcher at the Institute for Theoretical Physics, State University of Sćo 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).
