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.
Highlights
Introduction and summaryIn this paper we study three-dimensional N = 2 supersymmetric gauge theories [1, 2]
One interesting feature of 3d N = 2 theories is that gauge-invariant operators can decouple by strong-coupling effects, leading to emergent flavor symmetries in the IR
The theory has Nc − 1 independent monopole operators corresponding to the Cartan of the gauge group, most of them are lifted by the instanton-generated superpotential, with the exception of a a single unlifted monopole operator which is typically denoted by Y in the literature [1]
Summary
One interesting feature of the IR behavior of 3d N = 2 supersymmetric gauge theories is that there are often indications that strong-coupling effects make some operators free, and decouple from the rest of the system, in the IR In this case we need to subtract the corresponding degrees of freedom to discuss truly strongly-coupled interacting dynamics. We will see the strong evidence that such a decoupling of monopole operators do happen for 3d N = 2 SU(Nc) gauge theory with Nf flavors, for infinitely many values of Nc and Nf (see [6] for a similar analysis for U(Nc) gauge groups, which provided an inspiration for this paper). Gauging the SU(Nf )V flavor symmetry of U(Nc) SQCD, to obtain a quiver gauge theory with gauge group U(Nc) × SU(Nf ) (U(Nc) × U(Nf ))/U(1) This gauging changes the IR scaling dimensions, and changes the convergence bound for the S3 partition functions. Note that in three dimensions even the U(1) gauge group becomes strongly coupled in the IR, and we will find crucial differences from the case of U(Nc) SQCD analyzed in [6]
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