Vacuum structure and flavor symmetry breaking in supersymmetric SO(nc) gauge theories

Abstract

We determine the vacuum structure and phases of N = 1 theories obtained via a mass µ for the adjoint chiral superfield in N = 2, SO(n c ) SQCD. For large number of flavors these theories have two groups of vacua. The first exhibits dynamical breaking of flavor symmetry USp(2n f ) → U (n f ) and arises as a relevant deformation of a nontrivial superconformal theory. These are in the confined phase. The second group, in an IR-free phase with unbroken flavor symmetry, is produced from a Coulomb branch singularity with Seiberg's dual gauge symmetry. In the large-µ regime both groups of vacua are well-described by dual quarks and mesons, and dynamical symmetry breaking in the first group occurs via meson condensation. We follow the description of these vacua from weak to strong coupling and demonstrate a nontrivial agreement between the phases and the number of vacua in the two regimes. We construct the semiclassical monopole flavor multiplets and argue that their multiplicity is consistent with the number of N = 1 vacua.

Phases of SO(Nc) gauge theories with flavors

“…g 2s 2s TrΦ 2s (2.1) where the first two terms come from the N = 2 theory and the third term, W (Φ), can be described as a small perturbation of N = 2 SO(N c ) gauge theory [64,65,66,67,68,69,70,71,72,8,11] W (Φ) = where Φ ab is an adjoint scalar chiral superfield that plays the role of a deformation breaking N = 2 supersymmetry to N = 1 supersymmetry. Note that in [64] the coefficient for the mass term of quark in the tree superpotential is different from √ 2 used here, but it can be absorbed in the mass matrix and the only quadratic mass deformation for Φ with g 2 = µ (other parameters are vanishing) was considered in [64].…”

“…The strong coupling analysis has been done in [68,64]. Let us recall that the curve of 5 From this condition we see that when N f = 0, it is satisfied only when N ≤ 4.…”

Supersymmetric gauge theories with flavors and matrix models

“…In this subsection we will try to understand this vacuum structure of the gauge theory at both classical and quantum levels for a specific model (for more details, see [10,11,12,13,14,15]). For simplicity we will focus on U(N c ) theory with N f flavors and the following tree level superpotential 3…”

The Magnetic Monopoles Seventy-five Years Later

“…The class of models in question is N = 2 supersymmetric theories with SU, SO or USp gauge groups with quark hypermultiplets in various representations [17]- [25]. Moreover, the class of models in which one can make reliable analysis about their low-energy behavior, have increased enormously thanks to a more recent work on certain N = 1 models [26] with scalar multiplets in adjoint representation.…”

“…(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, .…”