Central Charges and Vacuum Moduli of 2d $\mathcal{N}=(0,4)$ Theories from Class $\mathcal{S}$

TL;DR

This paper explores 2d $ obreak ext{(0,4)}$ supersymmetric theories derived from 4d $ obreak ext{(2)}$ class $ obreak ext{S}$ theories, focusing on central charges, vacuum structures, and superconformal symmetries, with conjectural formulas and explicit analysis for $SU(2)$.

Contribution

It introduces conjectural formulas for central charges of these theories and analyzes their vacuum moduli spaces, especially for $SU(2)$ gauge groups, using Hilbert series computations.

Findings

Proposed formulas for central charges match Hilbert series results.

Identified distinct Higgs branches in the vacuum moduli space.

Confirmed consistency of superconformal R-symmetries with vacuum structures.

Abstract

We investigate 2d $\mathcal{N}=(0,4)$ supersymmetric theories obtained from a topologically-twisted reduction of 4d $\mathcal{N}=2$ class $\mathcal{S}$ theories on a Riemann surface. This study addresses subtle aspects of central charges, unbroken gauge groups, and emergent superconformal R-symmetries of these theories. Focusing on infrared vacuum structures, we propose conjectural formulas for the central charges. For theories with the gauge group $SU(2)$, we use a Lagrangian description to analyze the vacuum moduli spaces. In particular, we examine two distinct branches -- the special Higgs branch and the twisted Higgs branch -- by computing their Hilbert series, and find agreement with the proposed central charge formulas.