4D and 2D superconformal index with surface operator

TL;DR

This paper investigates the superconformal index of N=4 super-Yang-Mills theory on S^3 x S^1 with a half BPS surface operator, revealing how the index incorporates a 2D (4,4) SCFT on the defect and constructing a matrix model for computation.

Contribution

It introduces a matrix model to compute the superconformal index with a surface operator, integrating the 2D (4,4) SCFT on the defect with the 4D bulk theory.

Findings

Superconformal index remains unaffected by the surface operator's presence.

A matrix model is constructed for the index with the defect coupling.

The surface operator hosts a 2D (4,4) superconformal field theory.

Abstract

We study the superconformal index of the N=4 super-Yang-Milles theory on S^3 X S^1 with the half BPS superconformal surface operator (defect) inserted at the great circle of S^3. The half BPS superconformal surface operators preserve the same supersymmetry as well as the symmetry of the chemical potential used in the definition of the superconformal index, so the structure and the parameterization of the superconformal index remain unaffected by the presence of the surface operator. On the surface defect, a two-dimensional (4,4) superconformal field theory resides, and the four-dimensional superconformal index may be regarded as a superconformal index of the two-dimensional (4,4) superconformal field theory coupled with the four-dimensional bulk system. We construct the matrix model that computes the superconformal index with the surface operator when it couples with the bulk N=4 super-Yang-Milles theory through the defect hypermultiplets on it.