Dynamics of supersymmetric SU(n_c) and USp(2n_c) gauge theories

Abstract

We study dynamical flavor symmetry breaking in the context of a class of N = 1 supersymmetric SU (n c ) and U Sp(2n 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) × U (n f − r) groups for n f ≤ n c . In the r = 1 case the dynamical symmetry breaking is caused by the condensation of 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" which condense and induce confinement and the symmetry breaking. In U Sp(2n c ) theories with n f ≤ 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 U Sp(2n c ) theories, with larger numbers of quark flavors, besides the vacua with these properties, there exist also vacua with no flavor symmetry breaking.

The Magnetic Monopoles Seventy-five Years Later

“…(ii) The physics of the r vacua [22,24] indeed shows that the non-Abelian dual group SU(r) appear only for r ≤ N f 2 . This limit can be understood from the renormalization group: in order for a nontrivial r vacuum to exist, there must be at least 2 r massless matter flavor in the original, electric theory; (iii) Non-abelian vortices [29,31], which as we shall see are closely related to the concept of non-Abelian monopoles, require also an exact flavor group.…”

“…In N = 2, SU(N) SQCD with N f flavors, light non-Abelian monopoles with SU(r) dual gauge group appear for r ≤ N f 2 only. Such a limit clearly reflects the dynamics of the soliton monopoles under renormalization group: the effective low-energy gauge group must be either infrared free or conformally invariant, in order for the monopoles to emerge as recognizable low-energy degrees of freedom [22]- [24].…”

“…The exact sequence (28) assumes an important significance when we consider the system with a hierarchical symmetry breaking (24), As H is now completely broken the low-energy theory has vortices, classified by π 1 (H). If π 1 (G) = ∅, however, the full theory cannot have vortices.…”

“…(44). In SU(N c ) theories with N f flavors with generic masses, all N = 1 vacua arising this way have been completely classified [24,25]. For nearly equal quark masses they fall into classes r = 0, 1, .…”

“…We find that (i) We see the non-Abelian monopoles in action, in the generic r (2 ≤ r ≤ N f 2 ) vacua. See Table 2 taken from [24]. They behave perfectly as point-like particles, albeit in a dual, magnetic gauge system.…”