A worldsheet extension of O(d,d;Z)
Costas Bachas, Ilka Brunner, Daniel Roggenkamp

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.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models
