Abstract
We reexamine the vacuum structure of three-dimensional quantum chromodynamics (QCD3) with gauge group SU(N), Nf fundamental quark flavors, and a level-k Chern-Simons term. This analysis can be reliably carried out in the large-N, fixed Nf, k limit of the theory, up to certain assumptions that we spell out explicitly. At leading order in the large-N expansion we find Nf + 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 explicitly realizes 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. We show that 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.
Highlights
Important point is that there is no notion of chirality in three dimensions
We show that 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
Three-dimensional gauge theories with matter display different symmetries and different patterns of symmetry breaking than their four-dimensional cousins
Summary
We analyze QCD3, i.e. SU(N )k Yang-Mills-Chern-Simons theory coupled to Nf flavors of fundamental quarks, at leading order in the large-N expansion, while keeping k and Nf fixed. We use Lorentzian signature for the metric
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