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Orbifolds and Topological Defects

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Abstract

We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu–Schwarz and Ramond sectors of the orbifold theory, as well as bulk-boundary correlators from a novel, universal perspective. This entails a structure somewhat weaker than ordinary TFT, which however still describes a sector of the underlying conformal theory. The case of B-twisted Landau–Ginzburg models is discussed in detail, where we compute charge vectors and superpotential terms for B-type branes.

Our construction also works in the absence of supersymmetry and for generalised “orbifolds” that need not arise from symmetry groups. In general, this involves a natural appearance of Hochschild (co)homology in a 2-categorical setting, in which among other things we provide simple presentations of Serre functors and a further generalisation of the Cardy condition.

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Authors and Affiliations

  1. Arnold Sommerfeld Center for Theoretical Physics, LMU München, Theresienstraße 37, 80333, Munich, Germany

    Ilka Brunner & Daniel Plencner

  2. Excellence Cluster Universe, Boltzmannstraße 2, 85748, Garching, Germany

    Ilka Brunner & Daniel Plencner

  3. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794-3636, USA

    Nils Carqueville

Authors
  1. Ilka Brunner
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  2. Nils Carqueville
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  3. Daniel Plencner
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Correspondence to Daniel Plencner.

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Communicated by N. A. Nekrasov

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Brunner, I., Carqueville, N. & Plencner, D. Orbifolds and Topological Defects. Commun. Math. Phys. 332, 669–712 (2014). https://doi.org/10.1007/s00220-014-2056-3

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