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Matrix factorisations for rational boundary conditions by defect fusion
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 11 May 2015

Matrix factorisations for rational boundary conditions by defect fusion

  • Nicolas Behr1,2 &
  • Stefan Fredenhagen3 

Journal of High Energy Physics volume 2015, Article number: 55 (2015) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

A large class of two-dimensional \( \mathcal{N}=\left(2,\ 2\right) \) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the SU(3)/U(2) Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the SU(3)/U(2) model.

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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, U.K.

    Nicolas Behr

  2. Maxwell Institute for Mathematical Sciences, Edinburgh, U.K.

    Nicolas Behr

  3. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, D-14424, Golm, Germany

    Stefan Fredenhagen

Authors
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Correspondence to Nicolas Behr.

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ArXiv ePrint: 1407.7254

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Cite this article

Behr, N., Fredenhagen, S. Matrix factorisations for rational boundary conditions by defect fusion. J. High Energ. Phys. 2015, 55 (2015). https://doi.org/10.1007/JHEP05(2015)055

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  • Received: 13 January 2015

  • Accepted: 19 April 2015

  • Published: 11 May 2015

  • DOI: https://doi.org/10.1007/JHEP05(2015)055

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Keywords

  • D-branes
  • Conformal Field Models in String Theory
  • Tachyon Condensation
  • Topological Field Theories
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