A worldsheet extension of O(d,d;Z)

TL;DR

This paper extends the O(d,d;Z) symmetry to a semi-group in the context of superconformal interfaces between torus sigma models, linking fusion of interfaces to geometric transformations and T-duality.

Contribution

It introduces a semi-group extension of O(d,d;Q) describing fusion of superconformal interfaces, generalizing T-duality as a geometric transformation.

Findings

Fusion of interfaces is non-singular and corresponds to geometric integral transformations.

The semi-group of orbifold equivalences extends O(d,d;Z) and relates to ' deformations.

Topological interfaces form the same semi-group upon fusion.

Abstract

We study superconformal interfaces between N=(1,1) supersymmetric sigma models on tori, which preserve a 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(d,d;Q), 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 \alpha' deformation of the continuous O(d,d) symmetry of classical supergravity.