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Introduction to Supergravity and its Applications
出版済み 3-5週間でお届けいたします。
Author: Nastase, Horatiu (Universidade Estadual Paulista, Sao Paulo) Publisher: Cambridge University Press ISBN: 9781009445597 Cover: HARDCOVER Date: 2024年11月 DESCRIPTION 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. * Supergravity is used in many areas of current research, allowing readers to apply it to many different subjects * Self-contained, with little background assumed in typical prerequisites such as general relativity, supersymmetry * Provides an overview of most topics related to supergravity, at a digestible level, enabling students to read papers that involve supergravity * Summaries of important concepts and exercises follow each chapter, which will give a better understanding of the subject TABLE OF CONTENTS 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-Nunez 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.
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