A-D-E Singularity and the Seiberg-Witten Theory

TL;DR

This paper explores the Seiberg-Witten theory for ADE gauge groups, linking spectral curves, Toda lattice, and singularity theory to analyze exact solutions and superconformal fixed points.

Contribution

It establishes a connection between ADE singularities, spectral curves, and the Seiberg-Witten effective theory, providing new insights into superconformal fixed points and scaling exponents.

Findings

Superconformal fixed point characterized by ADE superpotential

Scaling exponents match previous theoretical predictions

Spectral curves relate to Toda lattice and singularity theory

Abstract

We study the low-energy effective theory of N=2 supersymmetric Yang-Mills theory with ADE gauge groups in view of the spectral curves of the periodic Toda lattice and the A-D-E singularity theory. We examine the exact solutions by using the Picard-Fuchs equations for the period integrals of the Seiberg-Witten differential. In particular, we find that the superconformal fixed point in the strong coupling region of the Coulomb branch is characterized by the ADE superpotential. We compute the scaling exponents, which agree with the previous results.