Abstract
We study 2+1 dimensional gauge theories with a Chern-Simons term and a fermion in the adjoint representation. We apply general considerations of symmetries, anomalies, and renormalization group flows to determine the possible phases of the theory as a function of the gauge group, the Chern-Simons level kk, and the fermion mass. We propose an inherently quantum mechanical phase of adjoint QCD with small enough kk, where the infrared is described by a certain Topological Quantum Field Theory (TQFT). For a special choice of the mass, the theory has {\cal N}=1 supersymmetry. There this TQFT is accompanied by a massless Majorana fermion – a Goldstino signaling spontaneous supersymmetry breaking. Our analysis leads us to conjecture a number of new infrared fermion-fermion dualities involving SUSU, SOSO, and SpSp gauge theories. It also leads us to suggest a phase diagram of SO/SpSO/Sp gauge theories with a fermion in the traceless symmetric/antisymmetric tensor representation of the gauge group.
Highlights
Consider adjoint QCD in 2+1 dimensions, that is Yang-Mills theory with a Chern-Simons term at level k and a Majorana fermion λ in the adjoint representation of the gauge group G
We study the low energy dynamics of this theory as a function of the gauge group G, the Chern-Simons level k and the mass Mλ of the fermion
Moving away from this supersymmetric point in the phase diagram can be interpreted as turning on a soft supersymmetry-breaking mass mλ for the gaugino
Summary
Consider adjoint QCD in 2+1 dimensions, that is Yang-Mills theory with a Chern-Simons term at level k and a Majorana fermion λ in the adjoint representation of the gauge group G. We denote by Gk a Chern-Simons term with gauge group G and level k. Moving away from this supersymmetric point in the phase diagram can be interpreted as turning on a soft supersymmetry-breaking mass mλ for the gaugino. This infrared theory coincides with the asymptotic phase at large negative mass.. At the supersymmetric point mλ = 0 supersymmetry is expected to be spontaneously broken for k < h/2 [14] This implies that at mλ = 0 there is a massless Majorana fermion (i.e. the Goldstino particle). For non- connected gauge groups, like SO(N )0, it has a zero-form magnetic symmetry, which can be spontaneously broken, leading to several vacua in the infinite volume system
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