The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories

Abstract

We derive the algebraic description of the Coulomb branch of 3d \mathcal{N}=4𝒩=4USp(2N)USp(2N) SQCD theories with N_fNf fundamental hypermultiplets and determine their low energy physics in any vacuum from the local geometry of the moduli space, identifying the interacting SCFTs which arise at singularities and possible extra free sectors. The SCFT with the largest moduli space arises at the most singular locus on the Coulomb branch. For N_f > 2NNf>2N (good theories) it sits at the origin of the conical variety as expected. For N_f =2NNf=2N we find two separate most singular points, from which the two isomorphic components of the Higgs branch of the UV theory emanate. The SCFTs sitting at any of these two vacua have only odd dimensional Coulomb branch generators, which transform under an accidental SU(2)SU(2) global symmetry. We provide a direct derivation of their moduli spaces of vacua, and propose a Lagrangian mirror theory for these fixed points. For 2 \leq N_f < 2N2≤Nf<2N the most singular locus has one or two extended components, for N_fNf odd or even, and the low energy theory involves an interacting SCFT of one of the above types, plus free twisted hypermultiplets. For N_f=0,1Nf=0,1 the Coulomb branch is smooth. We complete our analysis by studying the low energy theory at the symmetric vacuum of theories with N < N_f \le 2NN<Nf≤2N, which exhibits a local Seiberg-like duality.