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Three-dimensional gauge theories coupled to fermions can develop interestingnonperturbative dynamics. Here we study in detail the dynamics of $SU(N)$ gaugetheories coupled to a Dirac fermion in the rank-two symmetric and antisymmetricrepresentation. We argue that when the Chern-Simons level is sufficiently smallthe theory develops a quantum phase with an emergent topological field theory.When the Chern-Simons level vanishes, we further argue that a baryon condensesand hence baryon symmetry is spontaneously broken. The infrared theory thenconsists of a Nambu-Goldstone boson coupled to a topological field theory. Ourproposals also lead to new fermion-fermion dualities involving fermions intwo-index representations. We make contact between our proposals and somerecently discussed aspects of four-dimensional gauge theories. This leads us toa proposal for the domain wall theories of non-supersymmetric gauge theorieswith fermions in two-index representations. Finally, we discuss some aspects ofthe time-reversal anomaly in theories with a one-form symmetry.

Dynamics of QCD$_{3}$ with Rank-Two Quarks And Duality