Dynamical Symmetry Breaking in Supersymmetric SU(n_c) and USp(2n_c) Gauge Theories

TL;DR

This paper analyzes the phase and flavor symmetry breaking patterns in N=1 supersymmetric SU(n_c) and USp(2n_c) gauge theories, revealing how monopole and magnetic quark condensations induce confinement and symmetry breaking.

Contribution

It provides a detailed description of the vacuum structure and symmetry breaking mechanisms in supersymmetric gauge theories derived from N=2 models with mass perturbations, including novel insights into magnetic monopole behavior.

Findings

Flavor symmetry breaks to subgroups depending on vacuum r

Magnetic monopoles condense in specific representations causing symmetry breaking

Existence of vacua with unbroken global symmetry in larger flavor regimes

Abstract

We find the phase and flavor symmetry breaking pattern of each N=1 supersymmetric vacuum of SU(n_c) and USp(2 n_c) gauge theories, constructed from the exactly solvable N=2 theories by perturbing them with small adjoint and generic bare hypermultiplet (quark) masses. In SU(n_c) theories with n_f \leq n_c the vacua are labelled by an integer r, in which the flavor U(n_f) symmetry is dynamically broken to U(r) \times U(n_f-r) in the limit of vanishing bare hyperquark masses. In the r=1 vacua the dynamical symmetry breaking is caused by the condensation of magnetic monopoles in the n_f representation. For general r, however, the monopoles in the {}_{n_f}C_r representation, whose condensation could explain the flavor symmetry breaking but would produce too-many Nambu--Goldstone multiplets, actually "break up" into "magnetic quarks": the latter with nonabelian interactions condense and induce confinement and dynamical symmetry breaking. In USp(2n_c) theories with n_f \leq n_c + 1, the flavor SO(2n_f) symmetry is dynamically broken to U(n_f), but with no description in terms of a weakly coupled local field theory. In both SU(n_c) and USp(2 n_c) theories, with larger numbers of quark flavors, besides the vacua with these properties, there exist also vacua in free magnetic phase, with unbroken global symmetry.