Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

N=2 Generalized Superconformal Quiver Gauge Theory

Dimitri Nanopoulos, Dan Xie

TL;DR

This work connects 4D N=2 generalized SCFTs to the geometry of Riemann surface moduli, showing weakly coupled frames arise at stable nodal degenerations and that the gauge-coupling space is the Deligne–Mumford compactification $\bar{M}_{g,n}$. It provides an explicit degeneration-based algorithm to read off the weakly coupled gauge groups and matter content in any duality frame, grounded in Hitchin-system data and Coulomb/Higgs-branch matching. Through concrete examples, the authors demonstrate how to determine decoupled gauge sectors and matter content, including cases yielding SU, USp groups and an E6 theory. This framework unifies dual descriptions and links 4D SCFT data to the global geometry of moduli spaces, with potential extensions to other A-type quivers and non-Lagrangian sectors.

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.

N=2 Generalized Superconformal Quiver Gauge Theory

TL;DR

This work connects 4D N=2 generalized SCFTs to the geometry of Riemann surface moduli, showing weakly coupled frames arise at stable nodal degenerations and that the gauge-coupling space is the Deligne–Mumford compactification . It provides an explicit degeneration-based algorithm to read off the weakly coupled gauge groups and matter content in any duality frame, grounded in Hitchin-system data and Coulomb/Higgs-branch matching. Through concrete examples, the authors demonstrate how to determine decoupled gauge sectors and matter content, including cases yielding SU, USp groups and an E6 theory. This framework unifies dual descriptions and links 4D SCFT data to the global geometry of moduli spaces, with potential extensions to other A-type quivers and non-Lagrangian sectors.

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.

Paper Structure

This paper contains 9 sections, 49 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Review on counting Coulomb branch and Higgs branch dimensions
  3. Nodal curve and weakly coupled gauge theory description
  4. The gauge group and matter content
  5. Weakly coupled gauge group
  6. Matter content
  7. Examples
  8. Conclusion
  9. The Contribution to Higgs Branch of One Generic Puncture

Figures (6)

  • Figure 1: Left: A nodal curve. Right: The normalization of a.
  • Figure 2: A dual graph for the nodal curve in Figure \ref{['nodal']}.
  • Figure 3: Left: A torus with four marked points. Right: An irreducible nodal curve of a.
  • Figure 4: Left: The dual graph for the irreducible nodal curve of Figure \ref{['irreducible']}, we omit the genus $0$ on each vertex for simplicity, since for irreducible nodal curve, all components have genus zero. Right: Four dimensional gauge theory, we put a gauge group on the internal line, external lines represent the $U(1)$ flavor symmetries.
  • Figure 5: One weakly coupled gauge group
  • ...and 1 more figures