Metastable Vacua in Large-N QCD₃

Authors: Adi Armoni, Thomas T. Dumitrescu, Guido Festuccia, and Zohar Komargodski

Preprint number: UUITP-17/19

We reexamine the vacuum structure of three-dimensional quantum chromodynamics (QCD₃) with gauge group SU(N), N_f fundamental quark flavors, and a level-k Chern-Simons term. This analysis can be reliably carried out in the large-N, fixed N_f, k limit of the theory, up to certain assumptions that we spell out explicitly. At leading order in the large-N expansion we find N_f + 1 distinct, exactly degenerate vacuum superselection sectors with different patterns of flavor-symmetry breaking. The associated massless Nambu-Goldstone bosons are generically accompanied by topological Chern-Simons theories. This set of vacua contains many candidate phases previously proposed for QCD₃. At subleading order in the large-N expansion, the exact degeneracy between the different superselection sectors is lifted, leading to a multitude of metastable vacua. If we dial the quark masses, different metastable vacua can become the true vacuum of the theory, leading to a sequence of first-order phase transitions. This intricate large-N dynamics can be captured by the previously proposed bosonic dual theories for QCD₃, provided these bosonic duals are furnished with a suitable scalar potential. Interestingly, this potential must include terms beyond quartic order in the scalar fields.