Vacuum Structure and Spectrum ofN=2SupersymmetricSU(n)Gauge Theory

Abstract

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N = 2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n -1 hyperelliptic Riemann surfaces.

On non-commutative super Yang–Mills

“…The generalization of the Seiberg-Witten curve to the U(N) case seems to be [31,32,33] y 2 − 2P (z)y + 1 = 0 (2.12)…”

Exceptional SW geometry from ALE fibrations

“…The work of [1] was extended to other gauge groups: for example, to G = SU (n) in [2,3], to G = SO(2n + 1) in [4], and to G = SO(2n) in [5]. In these approaches, the curves are given in terms of the appropriate simple singularities W ADE [6], and are generically of the form y 2 = W 2 (x; u j ) − µ 2 , (1.1) with µ = Λ h ∨ , where h ∨ is the dual Coxeter number of G, and Λ is the quantum scale.…”

Nonsupersymmetric flux vacua and perturbed 𝒩 = 2 systems

“…In particular, the SU(N) Seiberg-Witten curve of gauge theory [48,49] is geometrically identified with the curve (3.14) underlying the Calabi-Yau. A T -duality along the compact circle in the uv-fiber, followed by a lift to M-theory, translates [50] this geometry into a system of an M5-brane which wraps the Riemann surface Σ SW and fills R 3,1 .…”