Central charges and vacuum moduli of 2d $\mathcal{N}=(0,4)$ theories from class $\mathcal{S}$

We investigate 2d \mathcal{N}=(0,4) 𝒩 = ( 0 , 4 ) supersymmetric theories obtained from a topologically-twisted reduction of 4d \mathcal{N}=2 𝒩 = 2 class \mathcal{S} 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) S U ( 2 ) , we use Lagrangian descriptions 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.