Gauging and Decoupling in 3d $\mathcal{N}=2$ dualities

TL;DR

This paper systematically analyzes the IR behavior and operator decoupling in 3d $ abla=2$ supersymmetric QCD with various gauge groups, exploring dualities, monopole effects, and implications for higher-dimensional theories.

Contribution

It provides a comprehensive study of decoupling phenomena and dualities in 3d $ abla=2$ SQCD across different gauge groups and limits, including new insights into monopole operators and defect classifications.

Findings

Decoupling of operators depends on gauge group and matter content.

Monopole operators play a crucial role in IR dynamics.

Gauging flavor symmetries affects the IR behavior and dualities.

Abstract

One interesting feature of 3d $\mathcal{N}=2$ theories is that gauge-invariant operators can decouple by strong-coupling effects, leading to emergent flavor symmetries in the IR. The details of such decoupling, however, depends very delicately on the gauge group and matter content of the theory. We here systematically study the IR behavior of 3d $\mathcal{N}=2$ SQCD with $N_f$ flavors, for gauge groups $\mathrm{SU}(N_c), \mathrm{USp}(2N_c)$ and $\mathrm{SO}(N_c)$. We apply a combination of analytical and numerical methods, both to small values of $N_c, N_f$ and also to the Veneziano limit, where $N_c$ and $N_f$ are taken to be large with their ratio $N_f/N_c$ fixed. We highlight the role of the monopole operators and the interplay with Aharony-type dualities. We also discuss the effect of gauging continuous as well as discrete flavor symmetries, and the implications of our analysis to the classification of $1/4$--BPS co-dimension 2 defects of 6d $(2,0)$ theories.