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

Read more

Summary

Generalized Hitchin’s equations and spectral curve

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

Field theory description and quartic superpotential
Hitchin fibration for moduli space of twisted Higgs bundle
Commuting matrices
General case: the use of holomorphy
Three irregular singularities: three gauge groups
Field theory analysis
Chiral ring relation for Maldacena-Nunez theory
General massless case
A sphere with three irregular singularities
Maldacena-Nunez theory
Conclusion
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.