A symmetry breaking scenario for QCD3

Abstract

We consider the dynamics of 2+1 dimensional SU(N) gauge theory with Chern-Simons level k and Nf fundamental fermions. By requiring consistency with previously suggested dualities for Nf ≤ 2k as well as the dynamics at k = 0 we propose that the theory with Nf> 2k breaks the U(Nf) global symmetry spontaneously to U(Nf/2 + k) × U(Nf/2 − k). In contrast to the 3+1 dimensional case, the symmetry breaking takes place in a range of quark masses and not just at one point. The target space never becomes parametrically large and the Nambu-Goldstone bosons are therefore not visible semi-classically. Such symmetry breaking is argued to take place in some intermediate range of the number of flavors, 2k < Nf< N∗(N, k), with the upper limit N∗ obeying various constraints. The Lagrangian for the Nambu-Goldstone bosons has to be supplemented by nontrivial Wess-Zumino terms that are necessary for the consistency of the picture, even at k = 0. Furthermore, we suggest two scalar dual theories in this range of Nf. A similar picture is developed for SO(N) and Sp(N) gauge theories. It sheds new light on monopole condensation and confinement in the SO(N) & Spin(N) theories.