A Symmetry Breaking Scenario for QCD3_3


We consider the dynamics of 2+1 dimensional SU(N)SU(N) gauge theory with Chern-Simons level kk and NfN_f fundamental fermions. By requiring consistency with previously suggested dualities for Nf≀2kN_f\leq 2k as well as the dynamics at k=0k=0 we propose that the theory with Nf>2kN_f> 2k breaks the U(Nf)U(N_f) global symmetry spontaneously to U(Nf/2+k)Γ—U(Nf/2βˆ’k)U(N_f/2+k)\times U(N_f/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<Nβˆ—(N,k)2k< N_f< N_*(N,k), with the upper limit Nβˆ—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=0k=0. Furthermore, we suggest two scalar dual theories in this range of NfN_f. A similar picture is developed for SO(N)SO(N) and Sp(N)Sp(N) gauge theories. It sheds new light on monopole condensation and confinement in the SO(N)SO(N) and Spin(N)Spin(N) theories.Comment: 25 pages, 6 figures. v2 added references, minor corrections, new material about symmetry breaking in U(1) gauge theorie

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