# N=2 Chern-Simons-Matter Theories Without Vortices

## TL;DR

This paper analyzes N=2 Chern-Simons-matter theories with specific gauge groups, revealing conditions under which the partition function simplifies and vortex configurations are absent, including a mass-deformed ABJM case.

## Contribution

It identifies a special condition (k1+k2=0) that simplifies the partition function and prevents vortex solutions in certain U(1) x U(1) Chern-Simons-matter theories.

## Key findings

- Partition function collapses to a single term when k1+k2=0.
- Theories with k1+k2=0 lack supersymmetric vortex configurations.
- Includes analysis of mass-deformed ABJM theory as a special case.

## Abstract

We study ${\cal N}=2$ Chern-Simons-matter theories with gauge group $U_{k_1}(1)\times U_{k_2}(1)$. We find that, when $k_1+k_2=0$, the partition function computed by localization dramatically simplifies and collapses to a single term. We show that the same condition prevents the theory from having supersymmetric vortex configurations. The theories include mass-deformed ABJM theory with $U(1)_{k}\times U_{-k}(1)$ gauge group as a particular case. Similar features are shared by a class of CS-matter theories with gauge group $U_{k_1}(1)\times \cdots \times U_{k_N}(1)$.