On the Quantum Moduli Space of N=2 Supersymmetric Gauge Theories

TL;DR

This paper constructs and verifies hyper-elliptic curves describing the quantum moduli spaces of vacua in N=2 supersymmetric SO(N_c) gauge theories with various flavors, revealing their structure, metrics, and spectra.

Contribution

It provides explicit construction and verification of the quantum moduli space curves for N=2 SO(N_c) theories, extending understanding of their structure and spectra.

Findings

Complete determination of moduli spaces for 2N_f < N_c-1

Parameterization and structure for 2N_f ≥ N_c-1

Exact metrics and spectra of stable states

Abstract

Families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of $N=2$ supersymmetric $SO(N_c)$ gauge theories coupled to $N_f$ flavors of quarks in the vector representation are constructed. The quantum moduli spaces for $2N_f < N_c-1$ are determined completely by imposing $R$-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue calculations. The quantum moduli spaces for $2N_f\geq N_c-1$ theories are parameterized and their general structure is worked out using residue calculations. The exact metrics on the quantum moduli spaces as well as the exact spectrum of stable massive states are derived. The results presented here together with recent results of Martinec and Warner provide a natural conjecture for the form of the curves for the other gauge groups.