Dynamics of QCD3 with rank-two quarks and duality

Abstract

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

Phases of two adjoints QCD3 and a duality chain

“…• SU (N 1 ) k 1 × U (N 2 ) k 2 + 2 ψ bif und 7 Note that for k 1 k 2 < 0, chain makes one of the rank decrease while other increase which is the unique feature of 2-node quiver theory compared to the simple gauge group case. 8 For the introduction to the quiver Chern-Simons theories, see for example [67].…”

“…2 Up to now nonperturbative quantum phase was investigated for the case of fermions in the fundamental, single real adjoint and sym/asym representations. The next natural generalization one could ask is to find a phase diagram when the matter content is two adjoint fermions since the existence of quantum phase was indicated in the case of SU (2) [7] together with the various hints from the 3+1 dimensional physics with single Dirac adjoint fermion [10][11][12][13]. But we were unable to replicate the previously successful apporach.…”

“…As a consequence, there are two different phase transitions upon varying the mass of fermions from negative to positive infinity. So far, the standard route to obtain a phase diagram consistent with various anomalies comes from finding two mutually non-local dual descriptions with common global symmetry [3][4][5][6][7][8][9]. Particularly, all these dual descriptions are in the semiclassical regime, in the sense that intermediate quantum phase could be accessed by weakly coupled analysis of dual descriptions.…”

“…Now the bosonization is carried out at the two distinguished critical points with two different mutually non-local dual descriptions [3]. This shape of the phase diagram has been successfully applied to the case of single adjoint/rank-two matter and some other cases such as single bifundamental fermions [4,5,[7][8][9]58] with various supporting checks [59][60][61][62][63][64][65]. (See [66] for the recent lecture note covering many aspects discussed above.)…”

“…We also find that 'Duality Chain' is successfully applicable for the following two types of theories. One is the dynamics of QCD 3 with arbitrary pair of fermions in the adjoint/rank-two representations which is the full generalization of the QCD 3 with single flavor fermion in adjoint/rank-two representation [4,7]. The other is the dynamics of the 2-node quiver gauge theory with two bifundamental fermions which is the generalization of the QCD 3 with the vector fermions [3] by gauging flavor symmetry [58].…”