Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs

TL;DR

This paper investigates exactly marginal operators in 3d $S$-fold SCFTs, analyzing their potential for supersymmetry enhancement and classifying the resulting superconformal theories.

Contribution

It identifies and analyzes exactly marginal operators in specific 3d $S$-fold SCFTs, revealing conditions for supersymmetry enhancement in the infrared.

Findings

Supersymmetry can be enhanced in certain 3d $S$-fold SCFTs.

Detailed superconformal index analysis supports supersymmetry enhancement.

Classification of marginal operators in gauged $T$-theories and their impact on IR supersymmetry.

Abstract

The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the $\mathcal{N}=2$ preserving exactly marginal operators of 3d $S$-fold SCFTs. Two families of such theories are considered: one is constructed by gauging the diagonal flavour symmetry of the $T(U(2))$ and $T(U(3))$ theories, and the other by gauging the diagonal flavour symmetry of the $T^{[2,1^2]}_{[2,1^2]}(SU(4))$ theory. In both families, it is possible to turn on a Chern--Simons level for each gauge group and to couple to each theory various numbers of hypermultiplets. The detailed analysis of the exactly marginal operators, along with the superconformal indices, allows us to determine whether supersymmetry gets enhanced in the infrared and to deduce the amount of supersymmetry of the corresponding SCFT.