A worldsheet extension of $ O\left( {d,d\left| \mathbb{Z} \right.} \right) $

Abstract

Abstract We study superconformal interfaces between $ \mathcal{N}=\left( {1,1} \right) $ supersymmetric sigma models on tori, which preserve a $ \widehat{u}{(1)^{2d }} $ current algebra. Their fusion is non-singular and, using parallel transport on CFT deformation space, it can be reduced to fusion of defect lines in a single torus model. We show that the latter is described by a semi-group extension of $ O\left( {d,d\left| \mathbb{Q} \right.} \right) $ ), and that (on the level of Ramond charges) fusion of interfaces agrees with composition of associated geometric integral transformations. This generalizes the well-known fact that T-duality can be geometrically represented by Fourier-Mukai transformations. Interestingly, we find that the topological interfaces between torus models form the same semi-group upon fusion. We argue that this semi-group of orbifold equivalences can be regarded as the α′ deformation of the continuous O(d, d) symmetry of classical supergravity.