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The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

Philip C. Argyres, Alon E. Faraggi

TL;DR

An exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional {ital N}=2 supersymmetric SU({ital n}) gauge theories is presented.

Abstract

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.

The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

TL;DR

An exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional {ital N}=2 supersymmetric SU({ital n}) gauge theories is presented.

Abstract

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.

Paper Structure

This paper contains 8 sections, 19 equations, 2 figures.

Table of Contents

  1. Classical Moduli Space.
  2. The $SU(n)$ Curve.
  3. Weak Coupling Monodromies.
  4. The Special Monodromies in Perturbation Theory.
  5. Metric on Moduli Space and Dyon Spectrum.
  6. Strong Coupling Monodromies.
  7. Acknowledgements.
  8. Note Added.

Figures (2)

  • Figure 1: Contours for a basis of cycles for the $SU(3)$ curve. The thick wavy lines represent the cuts, solid contours are on the first sheet, and dotted ones are on the second.
  • Figure 2: Contour unwinding after a long day.