# 2D Seiberg-like dualities with an adjoint matter

## TL;DR

This paper explores two-dimensional supersymmetric gauge theories with adjoint matter, proposing dualities analogous to higher-dimensional Seiberg dualities, and provides evidence through elliptic genus calculations and analysis of chiral rings.

## Contribution

It introduces and supports new 2D Seiberg-like dualities involving adjoint matter, with proofs via elliptic genus and analysis of chiral ring truncation.

## Key findings

- Elliptic genus matches for dual pairs, supporting the dualities.
- Nonperturbative chiral ring truncation observed in some dual theories.
- Mass gap behavior identified for theories with more fundamentals than the gauge rank.

## Abstract

We consider the analogue of Kutasov-Schwimmer-Seiberg duality for two-dimensional $\mathcal{N}=(2,2)$ $U(k)$ gauge theory with one adjoint $X$ with the superpotential $\Tr X^{l+1}$ and with fundamental and anti-fundamantal chiral multiplets. We give the evidences for the proposed dualities by analytically proving that the elliptic genus of dual pair coincides with each other. For some of the dual pairs flowing to the superconformal field theory, we show the nonperturbative truncation of the chiral ring. For the theory with one adjoint and $N_f >k$ fundamentals, we argue the theory exhibits mass gap.