# Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface

### Submission summary

 As Contributors: Heeyeon Kim Arxiv Link: https://arxiv.org/abs/2105.08783v3 (pdf) Date submitted: 2021-11-24 14:47 Submitted by: Kim, Heeyeon Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Mathematical Physics Approach: Theoretical

### Abstract

This paper studies supersymmetric ground states of 3d $\mathcal{N}=4$ supersymmetric gauge theories on a Riemann surface of genus $g$. There are two distinct spaces of supersymmetric ground states arising from the $A$ and $B$ type twists on the Riemann surface, which lead to effective supersymmetric quantum mechanics with four supercharges and supermultiplets of type $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,4)$ respectively. We compute the space of supersymmetric ground states in each case, graded by flavour and R-symmetries and in different chambers for real mass and FI parameters, for a large class of supersymmetric gauge theories. The results are formulated geometrically in terms of the Higgs branch geometry. We perform extensive checks of compatibility with the twisted index and mirror symmetry.

###### Current status:
Editor-in-charge assigned

### List of changes

1. On page 1, we added a paragraph after bullet points, which explicitly states our assumptions.

2. In section 1.1, we corrected the second sentence of the second paragraph, from "...finite-dimensional..." to "...finite-dimensional and compact...".

2. In the same section, we corrected the first sentence of the fourth paragraph, from "when the degree d is large.." to "when all the components of the degree d is large.."

3. Reference [28] added on page 20

4. At the bottom of page 37, we changed \times to \otimes

5. Above (A.1), we added "for p+q<= n".