Скачать с ютуб Dr. Andrea Santi (UiT): An introduction to supergravity in 11 dimensions – Part I в хорошем качестве

Dr. Andrea Santi (UiT): An introduction to supergravity in 11 dimensions – Part I

Dr. Andrea Santi (UiT). An introduction to supergravity in 11 dimensions – Part I. #20 seminar for the Grieg collaboration project. Abstract: The purpose of these lectures is to introduce d = 11 supergravity — the most important theory where Einstein’s General Relativity is combined with supersymmetry — and motivate the study of its supersymmetric back-grounds. I will discuss various geometric and Lie algebraic features of d = 11 supergravity in the language of differential geometry, without any knowledge of physics: emphasis will be placed on clarifying all the relevant definitions, along with examples. I will discuss the construction of a Lie superalgebra generated from spinor fields satisfying a certain PDE and the homogeneity theorem, which states that supergravity backgrounds preserving more than half of the supersymmetry are homogeneous. Finally, I will report on works in collaboration with José Figueroa-O’Farrill and Paul de Medeiros on the algebraic structure of this so-called Killing superalgebra and discuss applications to the determination of supersymmetric backgrounds. In particular, we will see that preserving more than half the supersymmetry implies the field equations of d = 11 supergravity. This is a bi-weekly seminar for the Grieg collaboration project SCREAM: Symmetry, Curvature Reduction, and EquivAlence Methods, funded by the Norwegian Financial Mechanism 2014-2021. The registration number of the project is 2019/34/H/ST1/00636. The focus of the project is on a broad class of differential geometric structures known as Cartan and parabolic geometries, which include conformal, projective, CR, and ODE geometry, (2, 3, 5)-distributions, parabolic contact structures, and many more besides. Moreover, we explore the interaction of these structures with a variety of subjects such as mechanical systems and geometric robots, the theory of integrable systems, and Penrose's Conformal Cyclic Cosmology programme. More information can be found in www.cft.edu.pl/grieg.