SciPost Phys. 5, 007 (2018) ·
published 23 July 2018

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We study 2+1 dimensional gauge theories with a ChernSimons 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
ChernSimons level $k$, and the fermion mass. We propose an inherently quantum
mechanical phase of adjoint QCD with small enough $k$, 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 fermionfermion dualities involving $SU$, $SO$, and $Sp$
gauge theories. It also leads us to suggest a phase diagram of $SO/Sp$ gauge
theories with a fermion in the traceless symmetric/antisymmetric tensor
representation of the gauge group.
Prof. Gomis: "We would like to first thank t..."
in Submission on Phases Of Adjoint QCD$_3$ And Dualities by Jaume Gomis, Zohar Komargodski, Nathan Seiberg