Abstract
We study low-energy dynamics of three-dimensional N=2SU(N) “chiral” gauge theories with F fundamental and F¯ anti-fundamental matters without a Chern–Simons term. Compared to a naive semi-classical analysis of the Coulomb branch, its quantum structure is highly richer than expected due to so-called “dressed” Coulomb branch (monopole) operators. We propose dualities and confinement phases for the “chiral” SU(N) theories. The theories with N>F>F¯ exhibit spontaneous supersymmetry breaking. The very many Coulomb branch operators generally remain exactly massless and are non-trivially mapped under the dualities. Some dualities lead to a novel duality between SU(N) and USp(2N˜) theories. For the 3d N=2SU(2) gauge theory with 2F doublets, there are generally F+2 “chiral” and “non-chiral” dual descriptions.
Highlights
Asymptotically-free gauge theories exhibit various phases depending on gauge groups, matter contents, space–time dimensions and so on
By further introducing the complex masses to more flavors, we find that a 3d N = 2 SU (2N ) gauge theory with (2N − a, 2F − a)fundamentals spontaneously breaks the supersymmetry
We investigated the quantum structure of the Coulomb moduli space of vacua in the 3d N = 2 SU (N ) “chiral” gauge theories with F fundamental and Fanti-fundamental matters
Summary
Asymptotically-free gauge theories exhibit various phases depending on gauge groups, matter contents, space–time dimensions and so on. We will introduce a “typical” set of the Coulomb branch coordinates for the 3d N = 2 SU (N ) gauge theories with chiral matter contents. There might be additional Coulomb branch operators which could appear in case of particular matter contents and the ranks of the gauge group. Notice that the effective Chern–Simons term is not generated for U (1) since the low-energy U (1) theory is vector-like That is why these Coulomb branches can be flat directions. For completeness of our paper, we study the “typical” Coulomb branch of the 3d N = 2 SU (2N + 1) theory with (F, F ) (anti-)fundamental matters, which needs a small modification of the previous analysis. Because the correct choice of the bare monopoles depend on the matter contents, we have to consider the dualities case-by-case
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