TOPOLOGICAL SIGMA MODELS AND AFFINE ALGEBRAS

Abstract

The worldvolume theory of k M5-branes at low energy limit in discrete light cone quantization is the little string theory. This LST could be understood via a N= (4,4) supersymmetric sigma model with target space being the moduli space of SU(k) N-instantons on R4. Then based upon Atiyah’s theorem, we could relate this sigma model with our sigma models to based loop groups. Topological and quasi-topological sectors are studied with correspondences to 1/2 and 1/4 BPS sectors of worldvolume theories. The double field extension of half- twisted (0,2) sigma model clarifies more on relations between T-dual sigma models and generalized complex structures. Generalized complex structure and its associated gauge algebra unifies the tangent and cotangent spaces of complex manifolds. We constructed the double sigma model on parallelized group manifold S1 x S3 thanks to its vanishing first chern character and bi-hermitian structure.