Metastable vacua in large-N QCD3
Adi Armoni, Thomas T. Dumitrescu, Guido Festuccia, Zohar Komargodski
Abstract
A bstract We reexamine the vacuum structure of three-dimensional quantum chromodynamics (QCD 3 ) 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 explicitly realizes many candidate phases previously proposed for QCD 3 . 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 QCD 3 , provided these bosonic duals are furnished with a suitable scalar potential. Interestingly, this potential must include terms beyond quartic order in the scalar fields.