Dynamics of Supersymmetric SU(n_c) and USp(2n_c) Gauge Theories

TL;DR

This paper investigates how flavor symmetries are dynamically broken in certain supersymmetric SU(n_c) and USp(2n_c) gauge theories, revealing mechanisms involving monopole and magnetic quark condensates that lead to confinement and symmetry breaking.

Contribution

It provides a detailed analysis of flavor symmetry breaking mechanisms in N=1 supersymmetric gauge theories derived from N=2 models, highlighting the roles of monopoles and magnetic quarks.

Findings

Flavor U(n_f) symmetry in SU(n_c) theories breaks to U(r)×U(n_f−r)

Monopole condensation causes symmetry breaking in specific cases

USp(2n_c) theories exhibit SO(2n_f) to U(n_f) symmetry breaking without weakly coupled descriptions

Abstract

We study dynamical flavor symmetry breaking in the context of a class of N=1 supersymmetric 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. We find that the flavor U(n_{f}) symmetry in SU(n_{c}) theories is dynamically broken to $U(r)\times U(n_{f}-r)$ groups for $n_f \leq n_c$. In the r=1 case the dynamical symmetry breaking is caused by the condensation of monopoles in the $\underline{n_{f}}$ representation. For general r, however, the monopoles in the $\underline{{}_{n_{f}}C_{r}}$ representation, whose condensation could explain the flavor symmetry breaking but would produce too-many Nambu--Goldstone multiplets, actually ``break up'' into ``magnetic quarks'' which condense and induce confinement and the 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 with no flavor symmetry breaking.