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

Costas Bachas; Ilka Brunner; Daniel Roggenkamp

doi:10.1007/jhep10(2012)039

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arXiv · 1205.4647

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

Costas Bachas·Ilka Brunner·Daniel Roggenkamp

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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 α' deformation of the continuous O(d,d) symmetry of classical supergravity.

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Costas Bachas, Ilka Brunner, Daniel Roggenkamp. 2013-06-21. A worldsheet extension of O(d,d;Z). https://doi.org/10.1007/jhep10(2012)039

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