Metastable Vacua in Large$N$ QCD$_3$
Abstract
We reexamine the vacuum structure of threedimensional quantum chromodynamics (QCD$_3$) with gauge group $SU(N)$, $N_f$ fundamental quark flavors, and a level$k$ ChernSimons 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 flavorsymmetry breaking. The associated massless NambuGoldstone bosons are generically accompanied by topological ChernSimons theories. This set of vacua contains 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 firstorder phase transitions. 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.01797
 Bibcode:
 2019arXiv190501797A
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 57 pages, 11 figures