M5 brane and four dimensional N=1 theories I

TL;DR

This paper explores the engineering of 4D N=1 theories via compactification of 6D (2,0) theory on Riemann surfaces, introducing a generalized Hitchin's equation with applications to Seiberg duality and dual theories.

Contribution

It proposes a generalized Hitchin's equation involving two Higgs fields for N=1 compactification and interprets regular punctures as nilpotent commuting pairs, connecting dualities to geometric degenerations.

Findings

Seiberg duality corresponds to different degeneration limits of the same Riemann surface.

Identifies five dual theories related to SU(N) SQCD with Nf=2N.

Regular punctures are characterized by nilpotent commuting pairs.

Abstract

Four dimensional N=1 theories are engineered by compactifying six dimensional (2,0) theory on a Riemann surface with regular punctures. A generalized Hitchin's equation involving two Higgs fields is proposed as the BPS equation for N=1 compactification. The puncture is interpreted as the singular boundary condition of this equation, and regular puncture is shown to be labeled by a nilpotent commuting pair. In this paper, we focus on a subset of regular puncture which is described by rotating branes representing N=2 puncture. As an application, we show that the Seiberg duality of SU(N) SQCD with Nf=2N and certain superpotential term is realized as different degeneration limits of the same punctured Riemann surface, and also find four more dual theories.