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LACES 2025 Lezioni Avanzate di Campi E Stringhe
Galileo Galilei Institute for Theoretical Physics, Arcetri Italy |
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Supergravity Daniel Waldram - Imperial College London |
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| Syllabus The idea of the course is to give an introduction to supergravity taking a fairly pragmatic approach to give you the tools that are useful in research, although all from a classical perspective.. It will be close in parts to the textbook "Supergravity" by Freedman and van Proeyen, though with a more geometrical focus. If time permits it will include some details on supersymmetric backgrounds and the structure of generalised geometry as a unifying description of supergravity. The rough syllabus (though we will probably adapt as the lectures progress) will be 1. Introduction: Symmetries, particles and representations of the Poincare group; Clifford algebras and spinors; Coleman-Mandula and Haag–Łopuszański–Sohnius theorems and global supersymmetry; local supersymmetry and supergravity. 2. Connections, torsion and G-structures Mathematical digression on frame bundles, affine connections, G-structures and intrinsic torsion, tools that will appear throughout. 3. Basic supergravity Minimal supergravity in D=4 and D=11; outline of proof of local supersymmetry and the structure of the supersymmetry algebra; discussion of superspace formulation of supergravity. 4. Minimal D=4 supergravity coupled to matter Chiral and vector multiplets; Kahler geometry, R-symmetry, Kahler-Hodge manifolds; superpotentials and moment maps. 5. Summary of supergravities in diverse dimensions Supersymmetry algebras and R-symmetry; matter manifolds, cones, symmetric spaces and special geometries; gaugings, the embedding tensor and more moment maps. 6. Supersymmetric backgrounds and compactification Fluxless Minkowski backgrounds, Killing spinors and special holonomy, Calabi-Yau, hyperKahler, G2 and Spin(7) geometries; AdS backgrounds with top-form fluxes, Sasaki-Einstein etc; general flux backgrounds and G-structures 7. Flux backgrounds and generalised geometry (if time) Unifying the bosonic symmetries and algebroids; generalised connection torsion and curvature; "D=11 as D=4" and conditions for supersymmetry; applications to moduli and AdS/cft References: - "Supergravity", Freedman and Van Proeyen, CUP (2012) - "Supergravity: From First Principles to Modern Applications",Dall'Agata and Zagermann, Springer (2021) - "Supergravity", Bernard de Wit, arXiv:hep-th/0212245 - "Introduction to Supersymmetry and Supergravity", Jan Louis at https://www.physik.uni-hamburg.de/th2/ag-louis/dokumente/lectures/ws-15-16/ws-15-susy-lecture-notes.pdf - "Introduction to Supergravity", Samtleben, https://saalburg.aei.mpg.de/wp-content/uploads/sites/25/2017/03/samtleben.pdf |
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Organisers: Lorenzo Bianchi Daniele Dorigoni Dario Francia Federico Galli Valentina Giangreco Puletti Stefano Massai |
Secretary: Annalisa Anichini Mauro Morandini Housing: Mirella Ridi Computer assistance: Alessio Attardi |
Sponsored by
 
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