Abstract
We conjecture infrared emergent $\mathcal{N}=4$ supersymmetry for a class of three-dimensional $\mathcal{N}=2$ $U(1)$ gauge theories coupled with a single chiral multiplet. One example is the case where $U(1)$ gauge group has the Chern-Simons level $-\frac{3}2$ and the chiral multiplet has gauge charge $+1$. Other examples are related to this example either by known dualities or rescaling the Abelian gauge field. We give three independent evidences for the conjecture: 1) exact match between the central charges of the $U(1)$ R-symmetry current and the $U(1)$ topological symmetry current, 2) semi-classical construction of the $\mathcal{N}=4$ stress-tensor multiplet, and 3) an IR duality between a direct product of the two copies of the 3d theory on the one hand, and an $\mathcal{N}=4$ theory obtained by gauging the diagonal $SU(2)$ flavor symmetry of the $T[SU(2)]$ theory, on the other. The duality in 3) follows from geometrical aspects of the 3d-3d correspondence.
Highlights
Symmetry has long been a fundamental guiding principle in theoretical physics
We give three independent pieces of evidence for the conjecture: (i) exact match between the central charges of the U(1) R-symmetry current and the U(1) topological symmetry current, (ii) semiclassical construction of the N 1⁄4 4 stresstensor multiplet, and (iii) an IR duality between a direct product of the two copies of the 3D theory, on the one hand, and an N 1⁄4 4 theory obtained by gauging the diagonal SU(2) flavor symmetry of the T1⁄2SUð2Þ
There is a different attractive possibility where supersymmetry is emergent in the infra-red (IR)—one starts with a theory with no supersymmetry in the UV, which flows to an IR fixed point with emergent supersymmetry
Summary
We conjecture infrared emergent N 1⁄4 4 supersymmetry for a class of three-dimensional N 1⁄4 2 U(1). Gauge theories coupled with a single chiral multiplet. One example is the case where the U(1) gauge group has the. 3 2 and the chiral multiplet has gauge charge þ1. Other examples are related to this example either by known dualities or rescaling the Abelian gauge field. We give three independent pieces of evidence for the conjecture: (i) exact match between the central charges of the U(1) R-symmetry current and the U(1) topological symmetry current, (ii) semiclassical construction of the N 1⁄4 4 stresstensor multiplet, and (iii) an IR duality between a direct product of the two copies of the 3D theory, on the one hand, and an N 1⁄4 4 theory obtained by gauging the diagonal SU(2) flavor symmetry of the T1⁄2SUð2Þ. The duality in (iii) follows from geometrical aspects of the 3D–3D correspondence
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