Explicit factorization of Seiberg-Witten curves with matter from random matrix models

TL;DR

This paper derives explicit formulas for the Seiberg-Witten curve moduli in U(N_c) gauge theories with matter using random matrix models, revealing new structural insights into the Coulomb branch and monopole dynamics.

Contribution

It provides a novel explicit factorization of Seiberg-Witten curves with matter from random matrix theory, enhancing understanding of gauge theory moduli.

Findings

Explicit expressions for moduli from matrix models.

Moduli are additive with matter and color number.

Revealed non-trivial structures of the gauge theory.

Abstract

Within the Dijkgraaf-Vafa correspondence, we study the complete factorization of the Seiberg-Witten curve for U(N_c) gauge theory with N_f<N_c massive flavors. We obtain explicit expressions, from random matrix theory, for the moduli, parametrizing the curve. These moduli characterize the submanifold of the Coulomb branch where all monopoles become massless. We find that the matrix model reveals some non-trivial structures of the gauge theory. In particular the moduli are additive with respect to adding extra matter and increasing the number of colors.