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 mathcal{N}=2 supersymmetry, we show that even when the monopole potential is irrelevant, the monopole-modified theory {mathcal{T}}_{mathfrak{M}} can exist and enjoy Seiberg-like dualities. We provide a renormalizable UV completion of {mathcal{T}}_{mathfrak{M}} and an electric-magnetic dual description {mathcal{T}}_{mathfrak{M}}^{prime } . We subject our proposal to various consistency checks such as mass deformations and Sb3 partition functions checks. We observe that {mathcal{T}}_{mathfrak{M}} is the S-duality wall of 4D mathcal{N}=2 SQCD. We also consider monopole-deformed theories with Chern-Simons couplings and their duals.
Highlights
On a two-sphere surrounding their insertion point
Long ago Polyakov [1] showed that monopole operators can appear in the potential, at the infrared fixed-point of an RG-flow triggered by Higgsing a gauge symmetry leading to confinement
In condensed-matter physics, quantum mechanical lattice models in two spatial dimensions admit, in the thermodynamic limit, interesting second-order quantum phase transitions which should be described by a (2 + 1)-dimensional conformal field theory (CFT) [2]. Such a CFT3 could for instance be a U(1) gauge theory with some number of fermionic and/or scalar charged matter fields
Summary
A possible way to reach TM is to start from the 4D USp(2Nc) SQCD theory with 2Nf fundamental flavors. The deformation by the monopole superpotential drives the theory to a non-trivial fixed point. This duality was tested in [26] at the level of the partition function on the squashed three-sphere Sb3 [44]. In the final U(Nc) theory these symmetries are broken by non-perturbative effects, namely by the original instanton and by an extra non-perturbative Affleck-Harvey-Witten contribution [24] associated to the breaking of the gauge group USp(2Nc) → U(Nc) These two non-perturbative contributions can be identified with the sum of the two fundamental monopoles, Wmon = M+ + M−, breaking U(1)A × U(1)T. Let us remark that, as long as the fixed point TM exists, we can study some of its properties — such as its moduli space or the anomalous dimensions of chiral operators — using Wmon even if such an operator is irrelevant at T0
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