Classification of supersymmetries

Details Classification of supersymmetries Classification of supersymmetries

2003-02-07

arxiv.org/abs/math-ph/0302016v2

Proceedings of the ICM, Beijing 2002, vol. 1, 319--344

Physics

Mathematical Physics

Scientific paper

In the first part of my talk I will explain a solution to the extension of Lie's problem on classification of "local continuous transformation groups of a finite-dimensional manifold" to the case of supermanifolds. (More precisely, the problem is to classify simple linearly compact Lie superalgebras, i.e. toplogical Lie superalgebras whose underlying space is a topological product of finite-dimensional vector spaces). In the second part I will explain how this result is used in a classification of superconformal algebras. The list consists of affine superalgebras and certain super extensions of the Virasoro algebra. In the third part I will discuss representation theory of affine superalgebras and its relation to "almost" modular forms. Furthermore, I will explain how the quantum reduction of these representations leads to a unified representation theory of super extensions of the Virasoro algebra. In the forth part I will discuss representation theory of exceptional simple infinite-dimensional linearly compact Lie superalgebras and will speculate on its relation to the Standard Model.

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