Generalized Hitchin system, Spectral curve and N=1 dynamics

TL;DR

<3-5 sentence high-level summary>We develop a general method to obtain $\mathcal{N}=1$ spectral curves from generalized Hitchin equations, engineering 4D theories via M5 branes on punctured Riemann surfaces. By introducing two Higgs fields $\Phi_1$ and $\Phi_2$ as sections of line bundles with $L_1\otimes L_2=K$, we construct coupled spectral data $\det(v-\Phi_1)=0$, $\det(w-\Phi_2)=0$ and a holomorphic link $w=h_1(z)v^{N-1}+\cdots+h_N(z)$, whose holomorphy fixes moduli and yields nontrivial IR dynamics. The framework recovers deformed moduli spaces, chiral ring relations, SUSY breaking, and even SQCD-like dualities across $SU(2)$ and $SU(N)$ examples, including Maldacena–Nunez theories, with explicit matches to known field-theoretic results. This approach reveals a tight bridge between generalized Hitchin systems, spectral curves, and 4D $\mathcal{N}=1$ dynamics, offering a powerful geometric lens on nonperturbative phenomena.

Abstract

A generalized Hitchin equation was proposed as the BPS equation for a large class of four dimensional N=1 theories engineered using M5 branes. In this paper, we show how to write down the spectral curve for the moduli space of generalized Hitchin equations, and extract interesting N=1 dynamics out of it, such as deformed modui space, chiral ring relation, SUSY breaking, etc. Holomorphy plays a crucial role in our construction.

Figures (2)

• Figure 1: A Riemann sphere with two singularities (left), its degeneration limit (upper-right) and the corresponding field theory quiver (lower-right).
• Figure 2: The newton polygon for irregular singularity. The red line represents the mass-deformed theory, and the black one represents the massless theory.