# Surface defects and elliptic quantum groups

## TL;DR

This paper proposes a brane construction of an integrable lattice model involving elliptic quantum groups, connecting surface defects in supersymmetric theories to transfer matrices derived from complex R-matrices.

## Contribution

It introduces a novel brane-based framework linking surface defects in 4D supersymmetric theories to elliptic quantum groups via an integrable lattice model.

## Key findings

- Surface defects act as transfer matrices in supersymmetric indices.
- The model incorporates Belavin's, Felder's, and Bazhanov-Sergeev-Derkachov-Spiridonov R-matrices.
- Establishes a connection between surface defects and elliptic quantum groups.

## Abstract

A brane construction of an integrable lattice model is proposed. The model is composed of Belavin's R-matrix, Felder's dynamical R-matrix, the Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining operators. This construction implies that a family of surface defects act on supersymmetric indices of four-dimensional $\mathcal{N} = 1$ supersymmetric field theories as transfer matrices related to elliptic quantum groups.