SUSY monopole potentials in 2+1 dimensions

TL;DR

The paper analyzes monopole operators in 2+1D ${\cal N}=2$ U($N_c$) SQCD with $N_f$ flavors, showing that a monopole potential ${\cal W}_{\rm mon}=\mathfrak{M}^++\mathfrak{M}^-$ yields a nontrivial fixed point ${\cal T}_{\mathfrak{M}}$ with a Seiberg-like dual ${\cal T}'_{\mathfrak{M}}$. The authors construct a renormalizable 3D UV completion using Ising-SCFTs, verify duality via ${S^3_b}$ partition functions and mass deformations, and relate ${\cal T}_{\mathfrak{M}}$ to the S-duality wall of 4D ${\cal N}=2$ SQCD at ${N_f=2N_c+2}$. They map the moduli spaces, analyze the dynamics across $(N_c,N_f)$, and extend to higher monopole potentials and CS couplings, providing a coherent web of dualities and RG flows. The work offers a robust framework to study monopole-induced deformations, offering concrete UV completions, exact partition-function checks, and connections to higher-dimensional dualities, with potential implications for nonperturbative dynamics in both SUSY and non-SUSY 2+1D systems.

Abstract

Gauge theories in 2+1 dimensions can admit monopole operators in the potential. Starting with the theory without monopole potential, if the monopole potential is relevant there is an RG flow to the monopole-deformed theory. Here, focusing on U(Nc) SQCD with Nf flavors and N=2 supersymmetry, we show that even when the monopole potential is irrelevant, the monopole-modified theory Tm can exist and enjoy Seiberg-like dualities. We provide a renormalizable UV completion of Tm and an electric-magnetic dual description Tm'. We subject our proposal to various consistency checks such as mass deformations and three-sphere partition functions checks. We observe that Tm is the S-duality wall of 4D N=2 SQCD. We also consider monopole-deformed theories with Chern-Simons couplings and their duals.

Figures (3)

• Figure 1: Schematic structure of RG flows that can lead to ${\cal T}_\mathfrak{M}$. The pink flow is a $\text{4D}\to\text{3D}$ reduction on $S^1$, while the red flow is a real mass deformation. The green flow is a deformation of ${\cal T}_0$ by ${\cal W}_\text{mon}$, which is relevant on the left but irrelevant on the right (and therefore it does not leave ${\cal T}_0$). The blue flow involves more degrees of freedom: the Ising-SCFT and extra free fields (see Section \ref{['superisi']}).
• Figure 2: Dynamics of $\mathcal{T}_\mathfrak{M}$ in various regions of the parameter space $N_c, N_f$. Blue line $N_f=\frac{4}{3}(N_c+1)$, green line $N_f = N_c + 2$, orange line $N_f = N_c + 1$.
• Figure 3: Qualitative RG diagram of the supposed minimal flow that can accommodate ${\cal T}_0$ and ${\cal T}_\mathfrak{M}$ in cases that ${\cal W}_\text{mon}$ is irrelevant in ${\cal T}_0$. Here $g$ is the gauge coupling and $\eta$ the monopole coupling in $\eta {\cal W}_\text{mon}$. The point ${\cal T}_\text{UV}$ is the weakly-coupled $U(N_c)$ SQCD with $N_f$ flavors, ${\cal T}_0$ is its IR fixed point, and ${\cal T}_\mathfrak{M}$ the non-trivial fixed point with monopole deformation turned on. The topology requires the existence of (at least) one unstable fixed point ${\cal T}_\text{us}$.