Introduction to Supergravity
Graduate course given at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and Tsinghua University in the spring of 2022
Dates: Every Wednesday & Friday 2022-03-16 ~ 06-03, 13:30-15:05 (UTC +8:00)
Venue: Conference room 3, Jinchunyuan West Building, Tsinghua Univ.
Description:
After a brief introduction to differential geometry and global supersymmetry, we will study minimal and extended supergravities in diverse dimensions. The course will be oriented towards applications of supergravities as backgrounds for supersymmetric quantum field theories, as well as in the AdS/CFT correspondence.
Prerequisites:
General Relativity or basic differential geometry, basic background in supersymmetry.
References:
- Supergravity, D. Z. Freedman and A. Van Proeyen, Cambridge University Press 2012.
Provisional Plan & Lecture Notes:
Lecture 1: Internal and spacetime symmetries, the Poincaré group
Lecture 2: Spinor representations
Lecture 3: Clifford algebra and gamma matrix technology
Lecture 4: Majorana spinors, $\mathcal{N}=1$ global supersymmetry
Lecture 5: $\mathcal{N}=1$ algebra and general invariant Lagrangians
Lecture 6: Representations of extended supersymmetry, vielbein and covariant derivatives
Lecture 7: Curvature tensor, first and second order formalisms for theories of gravity
Lecture 8: Simple $\mathcal{N}=1$ supergravity
Lecture 9: $\mathcal{N}=1$ supergravity algebra, D=11 supergravity
Lecture 10: General gauge theory: transformations, covariant derivatives and curvatures
Lecture 11: Gauged spacetime translations, transformation of covariant quantities.
Lecture 12: Survey of supergravity theories in diverse dimensions
Lecture 13: Complex and Kähler geometry
Lecture 14: $\mathcal{N}=1$ global supersymmetry multiplet calculus
Lecture 15: Conformal approach to Einstein gravity
Lecture 16: Conformal approach to $\mathcal{N}=1$ supergravity
Lecture 17: Coupling matter to $\mathcal{N}=1$ supergravity
Lecture 18: Projective Kähler manifolds: from conformal to Poincaré supergravity
Lecture 19: $\mathcal{N}=2$ supersymmetry and supergravity
Lecture 20: Supergravity solutions and the black hole attractor mechanism
Lecture 21: AdS/CFT correspondence and holographic correlation functions
Lecture 22: Off-shell supergravities and supersymmetric QFT backgrounds