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

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