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.
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Gomis, J., Le Floch, B. M2-brane surface operators and gauge theory dualities in Toda. J. High Energ. Phys. 2016, 183 (2016). https://doi.org/10.1007/JHEP04(2016)183
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DOI: https://doi.org/10.1007/JHEP04(2016)183