A note on 3D $ \mathcal{N} $ = 2 dualities: real mass flow and partition function

Abstract

We study two well-known classes of dualities in three dimensional N = 2 supersymmetric field theories. In the first class there are non trivial interactions involving monopole operators while in the second class the dual gauge theories have Chern-Simons terms in the action. An RG flows connecting the first dual pair to the second one has been studied in the past and tested on the partition function on the squashed three sphere. Recently an opposite RG flow connecting the second dual pair to the first one has been studied in the case of unitary gauge groups. In this paper we study this flow on the partition function on the squashed three sphere. We verify that the equality between the partition functions of the original dual models is preserved in the IR, where the other dual pair is reached. We generalize the analysis to the case of symplectic and of orthogonal groups.

Chern-Simons and RG flows: contact with dualities

“…On the electric side we have a chiral U(k) k/2 gauge theory with k fundamental and no anti-fundamental flavors. This theory is dual to a gauge singlet [10,12,13,34,35], corresponding to the monopole of the electric theory with magnetic flux (1, 0, . .…”

“…In appendix A we review some aspects of the partition function on the squashed three sphere, summarize the integral identities that we used in the paper and discuss the relation between the partition function and the contact terms. In appendix B we discuss some RG flow between dual pairs, generalizing the reverse flows of [10][11][12].…”

4D/3D reduction of dualities: mirrors on the circle

“…The details of the reduction -involving the superpotential W η , the real mass flow and the non-trivial vacua -depend on the nature of the gauge group and the matter content. We refer the reader to the papers [5,7,[20][21][22] for more details and explicit examples. Let us note that the 4D dualities on a finite circle, with non-perturbative superpotentials W η , give rise to new, effectively 3 dimensional dualities, which are interesting in their own right.…”

A journey to 3d: exact relations for adjoint SQCD from dimensional reduction

“…It would be desirable to extend the dualities studied in this paper by considering a chiral flavour sector, as done for the case without adjoint in [6]. This would also be useful in studying the inverse flow from the dualities with CS terms in [26,27] to Kim-Park duality, along the lines of [41][42][43]. On the partition function this corresponds to deriving the identity (3.21) from (3.22).…”