Phases of N=1 Supersymmetric SO/Sp Gauge Theories via Matrix Model

Abstract

We extend the results of Cachazo, Seiberg and Witten to N=1 supersymmetric gauge theories with gauge groups SO(2N), SO(2N+1) and Sp(2N). By taking the superpotential which is an arbitrary polynomial of adjoint matter Φas a small perturbation of N=2 gauge theories, we examine the singular points preserving N=1 supersymmetry in the moduli space where mutually local monopoles become massless. We derive the matrix model complex curve for the whole range of the degree of perturbed superpotential. Then we determine a generalized Konishi anomaly equation implying the orientifold contribution. We turn to the multiplication map and the confinement index K and describe both Coulomb branch and confining branch. In particular, we construct a multiplication map from SO(2N+1) to SO(2KN-K+2) where K is an even integer as well as a multiplication map from SO(2N) to SO(2KN-2K+2) (K is a positive integer), a map from SO(2N+1) to SO(2KN-K+2) (K is an odd integer) and a map from Sp(2N) to Sp(2KN+2K-2). Finally we analyze some examples which show some duality: the same moduli space has two different semiclassical limits corresponding to distinct gauge groups.

55pp; two paragraphs in page 19 added to clarify the relation between confinement index and multiplication map index, refs added and to appear in JHEP; Konishi anomaly equations corrected and some comments on the degenerated cases for SO(7) and SO(8) added

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Cited by in corpus (18)

• On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
• Effective Superpotentials via Konishi Anomaly
• Constructing Gauge Theory Geometries from Matrix Models
• Cubic curves from matrix models and generalized Konishi anomalies
• Branches of N=1 Vacua and Argyres-Douglas Points
• Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models
• Phases of N=1 USp(2N_c) Gauge Theories with Flavors
• Phases of N=1 SO(N_c) Gauge Theories with Flavors
• Matrix Model Description of Baryonic Deformations
• Exact U(N_c)-> U(N_1)xU(N_2) factorization of Seiberg-Witten curves and N=1 vacua
• On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
• On Confinement Index
• Matrix Models, Monopoles and Modified Moduli
• On Effective Superpotentials and Compactification to Three Dimensions
• More on N=1 Matrix Model Curve for Arbitrary N
• Chiral rings, anomalies and loop equations in N=1* gauge theories
• The Matrix Model Curve Near the Singularities
• Effective superpotential for U(N) with antisymmetric matter