Flavored surface defects in 4d N=1 SCFTs

TL;DR

This paper explores supersymmetric surface defects in 4d N=1 SCFTs derived from 6d conformal matter, revealing new flavor symmetries and analyzing their properties via superconformal indices and difference operators.

Contribution

It introduces a novel construction of surface defects in 4d N=1 theories from 6d compactifications and studies their duality properties using superconformal indices.

Findings

Defects carry SU(2) flavor symmetry not present in the 4d model.

Superconformal index acts as a kernel for difference operators related to defects.

Index computations verify dualities and the 6d to 4d correspondence.

Abstract

We discuss supersymmetric surface defects in compactifications of six dimensional minimal conformal matter of type SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions are N=1 quiver gauge theories with SU(3) and SU(4) gauge groups respectively. The defects are engineered by giving space-time dependent vacuum expectation values to baryonic operators. We find evidence that in the case of SU(3) minimal conformal matter the defects carry SU(2) flavor symmetry which is not a symmetry of the four dimensional model. The simplest case of a model in this class is SU(3) SQCD with nine flavors and thus the results suggest that this admits natural surface defects with SU(2) flavor symmetry. We analyze the defects using the superconformal index and derive analytic difference operators introducing the defects into the index computation. The duality properties of the four dimensional theories imply that the index of the models is a kernel function for such difference operators. In turn, checking the kernel property constitutes an independent check of the dualities and the dictionary between six dimensional compactifications and four dimensional models.