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

Abstract

We study N = 2 Chern-Simons-matter theories with gauge group U k 1 (1) × 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 ×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).

Exact results and Schur expansions in quiver Chern-Simons-matter theories

“…The partition function, as written in (3.17), is invariant under k ↔ −k but the final expression (3.18) is not because, without loss of generality, we have assumed k > 0 in the intermediate steps. The result agrees with [9], where the answer was obtained in a straightforward way using a change of variables x = x − y in (3.17). Nevertheless, with our approach we can consider the more general case with arbitrary rational k 1 and k 2 , which corresponds to deform the gravity dual by a Romans mass F 0 = k 1 + k 2 , cfr.…”

“…In contrast to previous works following a similar approach to the one in our first part of the paper [7][8][9], our study will include quiver Chern-Simons-matter theories. In this way, in this first part, contained in section 3, we compute exactly the partition functions of various examples of Chern-Simons-matter theories on the three-sphere, systematically exploiting and interpreting the above mentioned result by Mordell [6].…”

Exact results and Schur expansions in quiver Chern-Simons-matter theories

“…The result agrees with [9], where the answer was obtained in a straightforward way using a change of variables x = x − y in (3.17). Nevertheless, with our approach we can consider the more general case with arbitrary rational k 1 and k 2 , which corresponds to deform the gravity dual by a Romans mass F 0 = k 1 + k 2 , cfr.…”

“…In contrast to previous works following a similar approach to the one in our first part of the paper [7][8][9], our study will include quiver Chern-Simons-matter theories. In this way, in this first part, contained in Section 3, we compute exactly the partition functions of various examples of Chern-Simons-matter theories on the three-sphere, systematically exploiting and interpreting the above mentioned result by Mordell [6].…”