N = 2 Chern-Simons-matter theories without vortices

Abstract

We study N = 2 Chern-Simons-matter theories with gauge group U<SUB>k₁</SUB>(1)×U<SUB>k₂</SUB>(1). We find that, when k₁ + k₂ = 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× U_−k(1) gauge group as a particular case. Similar features are shared by a class of CS-matter theories with gauge group U<SUB>k₁</SUB>(1)×⋯×U<SUB>k_N</SUB>(1).