Complex Structures, T-duality and Worldsheet Instantons in Born Sigma Models

Abstract

Abstract We study generalized (doubled) structures in 2D-dimensional Born geometries in which T-duality symmetry is manifestly realized. We show that spacetime structures of Kähler, hyperkähler, bi-hermitian and bi-hypercomplex manifolds are implemented in Born geometries as generalized (doubled) structures. We find that the Born structures and the generalized Kähler (hyperkähler) structures appear as subalgebras of bi-quaternions ℂ × ℍ and split-tetra-quaternions ℍ × Spℍ. We investigate the nature of T-duality for the worldsheet instantons in Born sigma models. This manuscript is based on the original paper [1].