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.
Highlights
Closely related methods which are used very successfully in finding solutions for general N = 2 theories
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
One is the type IIA brane construction and its M theory lift [3], and the other one is using the connection of the Seiberg-Witten solution and integrable system [4,5,6], in particular, Hitchin system is playing a crucial role in finding solutions
Summary
Four dimensional N = 1 theories can be derived by compactifying six dimensional (2, 0) theory on a punctured Riemann surface. We only consider locally N = 2 punctures, namely only one of the Higgs fields is singular at a puncture, with the same types of singularities as in [6, 31]. It is proposed in [11] that the following generalized Hitchin equations are the BPS equations for these N = 1 compactifications: DzΦ1 = DzΦ2 = 0, [Φ1, Φ2] = 0, Fzz + [Φ1, Φ∗1]h1 + [Φ2, Φ∗2]h2 = 0,. The purpose of this paper is to try to use spectral curve to understand this moduli space and learn interesting IR dynamics of field theory
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