Intersecting Surface Defects and Two-Dimensional CFT

TL;DR

This paper studies intersecting surface defects in 4D N=2 gauge theories, characterizes their coupled 4d/2d/0d theories, and proposes a link between their partition functions and Liouville/Toda CFT correlators.

Contribution

It introduces a framework for analyzing intersecting surface defects in 4D N=2 theories and establishes a conjectured correspondence with Liouville/Toda conformal field theories.

Findings

Constructed supersymmetric intersecting surface defects preserving two supercharges.

Identified the coupled 4d/2d/0d theories describing these defects.

Conjectured an explicit relation between partition functions and Liouville/Toda CFT correlation functions.

Abstract

We initiate the study of intersecting surface operators/defects in four-dimensional quantum field theories (QFTs). We characterize these defects by coupled 4d/2d/0d theories constructed by coupling the degrees of freedom localized at a point and on intersecting surfaces in spacetime to each other and to the four-dimensional QFT. We construct supersymmetric intersecting surface defects preserving just two supercharges in N = 2 gauge theories. These defects are amenable to exact analysis by localization of the partition function of the underlying 4d/2d/0d QFT. We identify the 4d/2d/0d QFTs that describe intersecting surface operators in N = 2 gauge theories realized by intersecting M2-branes ending on N M5-branes wrapping a Riemann surface. We conjecture and provide evidence for an explicit equivalence between the squashed four-sphere partition function of these intersecting defects and correlation functions in Liouville/Toda CFT with the insertion of arbitrary degenerate vertex operators, which are labeled by representations of SU(N).