N=2 Generalized Superconformal Quiver Gauge Theory

TL;DR

This paper explores the relationship between four-dimensional N=2 superconformal theories and the geometry of punctured Riemann surfaces, revealing that the gauge coupling space corresponds to the Deligne-Mumford compactification of the moduli space.

Contribution

It establishes a precise correspondence between weakly coupled gauge groups in N=2 theories and stable nodal curves in the moduli space, providing an algorithm for duality analysis.

Findings

Gauge coupling space is the Deligne-Mumford compactification ar{M}_{g,n}

Weakly coupled gauge groups correspond to stable nodal curves

Provides an algorithm for determining gauge groups and matter content

Abstract

Four dimensional N=2 generalized superconformal field theory can be defined by compactifying six dimensional (0,2) theory on a Riemann surface with regular punctures. In previous studies, gauge coupling constant space is identified with the moduli space of punctured Riemann surface M_{g,n}. We show that the weakly coupled gauge group description corresponds to a stable nodal curve, and the coupling space is actually the Deligne-Mumford compactification \bar{M}_{g,n}. We also give an algorithm to determine the weakly coupled gauge group and matter content in any duality frame.