N = 2 $$\mathcal{N}=2$$ Chern-Simons-matter theories without vortices

Abstract

Abstract We study N = 2 $$\mathcal{N}=2$$ Chern-Simons-matter theories with gauge group U k 1 1 × U k 2 1 $${U}_{k_1}(1)\times {U}_{k2}(1)$$ . 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 × 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 × ⋯ × U k N 1 $${U_k}_{{}_1}(1)\times \cdots \times {U}_{k_N}(1)$$