On the Geometric Interpretation of N = 2 Superconformal Theories

TL;DR

This paper clarifies the geometric interpretation of N=2 superconformal theories, resolving key issues and identifying their geometric content, including insights into mirror symmetry and phase diagram features.

Contribution

It provides a detailed analysis of the phase structure of N=2 superconformal theories, offering a natural resolution to the mirror symmetry of rigid Calabi-Yau manifolds.

Findings

Identified geometric content of N=2 superconformal theories

Resolved the mirror of rigid Calabi-Yau manifolds

Highlighted subtle features via models with unusual phase diagrams

Abstract

We clarify certain important issues relevant for the geometric interpretation of a large class of N = 2 superconformal theories. By fully exploiting the phase structure of these theories (discovered in earlier works) we are able to clearly identify their geometric content. One application is to present a simple and natural resolution to the question of what constitutes the mirror of a rigid Calabi-Yau manifold. We also discuss some other models with unusual phase diagrams that highlight some subtle features regarding the geometric content of conformal theories.