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M2-brane surface operators and gauge theory dualities in Toda

  • Jaume Gomis
  • Bruno Le FlochEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We give a microscopic two dimensional \( \mathcal{N} \) = (2, 2) gauge theory description of arbitrary M2-branes ending on N f M5-branes wrapping a punctured Riemann surface. These realize surface operators in four dimensional \( \mathcal{N} \) = 2 field theories. We show that the expectation value of these surface operators on the sphere is captured by a Toda CFT correlation function in the presence of an additional degenerate vertex operator labelled by a representation \( \mathrm{\mathcal{R}} \) of SU(N f ), which also labels M2-branes ending on M5-branes. We prove that symmetries of Toda CFT correlators provide a geometric realization of dualities between two dimensional gauge theories, including \( \mathcal{N} \) = (2, 2) analogues of Seiberg and Kutasov-Schwimmer dualities. As a bonus, we find new explicit conformal blocks, braiding matrices, and fusion rules in Toda CFT.

Keywords

Supersymmetry and Duality Conformal and W Symmetry M-Theory Extended Supersymmetry 

Notes

Open Access

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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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Laboratoire de Physique Théorique de l’ École Normale Supérieure, (Unité mixte (UMR 8549) du CNRS et de l’ENS, Paris)ParisFrance

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