Orientifolds and Mirror Symmetry

TL;DR

This paper explores parity symmetries, orientifolds, and mirror symmetry in various N=2 supersymmetric quantum field theories, providing a comprehensive analysis of their structures, anomalies, and dualities across different models.

Contribution

It offers a detailed study of orientifolds and mirror pairs in N=2 theories, extending geometric correspondences to include unorientable worldsheets and analyzing multiple model realizations.

Findings

Complete analysis of parity symmetries in N=2 minimal models

Identification of mirror pairs of orientifolds across models

Global understanding of orientifolds and D-branes in supersymmetric theories

Abstract

We study parity symmetries and crosscap states in classes of N=2 supersymmetric quantum field theories in 1+1 dimensions, including non-linear sigma models, gauged WZW models, Landau-Ginzburg models, and linear sigma models. The parity anomaly and its cancellation play important roles in many of them. The case of the N=2 minimal model are studied in complete detail, from all three realizations -- gauged WZW model, abstract RCFT, and LG models. We also identify mirror pairs of orientifolds, extending the correspondence between symplectic geometry and algebraic geometry by including unorientable worldsheets. Through the analysis in various models and comparison in the overlapping regimes, we obtain a global picture of orientifolds and D-branes.