CT-DUALITY AS A LOCAL PROPERTY OF THE WORLDSHEET

Abstract

In this present article, we study the local features of the worldsheet in the case when probe bosonic string moves in antisymmetric background field. We generalize the geometry of surfaces embedded in spacetime to the case when the torsion is present. We define the mean extrinsic curvature for spaces with Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, the field equation is just the equality of mean extrinsic curvature and extrinsic mean torsion, which we call CT-duality. To the worldsheet described by this relation we will refer as CT-dual surface.