M2-brane surface operators and gauge theory dualities in Toda

TL;DR

This paper connects M2-brane surface operators in 4D N=2 theories with Toda CFT correlators, revealing gauge theory dualities and providing new conformal blocks and fusion rules.

Contribution

It offers a microscopic 2D gauge theory description of M2-branes ending on M5-branes and links surface operator expectation values to Toda CFT correlators, uncovering dualities and new conformal data.

Findings

Surface operator expectation values match Toda CFT correlators.

Identifies gauge theory dualities via Toda CFT symmetries.

Provides explicit conformal blocks, braiding matrices, and fusion rules.

Abstract

We give a microscopic two dimensional ${\cal N}=(2,2)$ 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 ${\cal N}=2$ 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 ${\cal R}$ 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 ${\cal N}=(2,2)$ analogues of Seiberg and Kutasov--Schwimmer dualities. As a bonus, we find new explicit conformal blocks, braiding matrices, and fusion rules in Toda CFT.