Coulomb Phase ofN=2Supersymmetric QCD

Abstract

We present an explicit non-perturbative solution of N =2 supersymmetric SU (N ) gauge theory with N f ≤ 2N flavors generalizing results of Seiberg and Witten for N = 2.

The Coulomb branch of N = 1 supersymmetric gauge theory with adjoint and fundamental matter

“…(10) is identical to the family of curves describing N = 2 SU(N c ) SUSY QCD with lN f fundamental hypermultiplets [8]. Away from singular points the infrared limit is just a free field theory of photons, neutral scalars and their superpartners, and thus automatically has N = 2 SUSY.…”

“…The arguments are a straightforward generalization of those in Ref. [8]. We assume that the curve is hyperelliptic, and consider first the case lN f = N c .…”

Supersymmetry and strongly coupled gauge theories

“…For the generic such theory, the S-duality relations no longer identify all ultrastrong coupling points with weak coupling points. This is illustrated in Figure 2 which shows a fundamental domain for the S-duality group of SU (n) n ≥ 3 d = 4 N = 2 superQCD [17] which is an index three subgroup of SL(2, Z). Note that a point (τ = 0) with g = ∞ is included in the domain.…”

The Magnetic Monopoles Seventy-five Years Later

“…(20). One might argue that there is only one monopole, as all the degenerate solutions are related by the unbroken gauge group H = SU(2).…”

“…This is how we know that the non-Abelian monopoles exist in fully quantum theories [21]: in the so-called r-vacua of softly broken N = 2, SU(N) gauge theory, the light monopoles appear as the dominant infrared degrees of freedom and interact as pointlike particles having the charges of a fundamental multiplet r of an effective, dual SU(r) gauge group. In an SU(3) gauge theory broken to SU(2) × U(1) as in (20), with an appropriate number of quark multiplets (N f ≥ 4), for instance, light magnetic monopoles carrying the charges…”