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

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.

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Correspondence to D. Roggenkamp.

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ArXiv ePrint: 1205.4647

Unité mixte de recherche (UMR 8549) du CNRS et de l’ENS, associée à l’Université Pierre et Marie Curie et aux fédérations de recherche FR684 et FR2687.

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Bachas, C., Brunner, I. & Roggenkamp, D. A worldsheet extension of \( O\left( {d,d\left| \mathbb{Z} \right.} \right) \) . J. High Energ. Phys. 2012, 39 (2012). https://doi.org/10.1007/JHEP10(2012)039

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Keywords

  • Conformal and W Symmetry
  • Conformal Field Models in String Theory
  • D-branes