Permutation Orientifolds

TL;DR

This paper constructs and analyzes permutation orientifolds in rational conformal field theory, comparing algebraic and geometric approaches, and explores their realization in Landau Ginzburg models with matrix factorizations.

Contribution

It introduces a systematic construction of permutation orientifolds in rational CFT and connects these with geometric and Landau Ginzburg descriptions.

Findings

Constructed crosscap states for permutation orientifolds.

Compared CFT results with geometric interpretations.

Matched Landau Ginzburg matrix factorizations with crosscap states.

Abstract

We consider orientifold actions involving the permutation of two identical factor theories. The corresponding crosscap states are constructed in rational conformal field theory. We study group manifolds, in particular the examples $SU(2) \times SU(2)$ and $U(1)\times U(1)$ in detail, comparing conformal field theory results with geometry. We then consider orientifolds of tensor products of N=2 minimal models, which have a description as coset theories in rational conformal field theory and as Landau Ginzburg models. In the Landau Ginzburg language, B-orientifolds and D-branes are described in terms of matrix factorizations of the superpotential. We match the factorizations with the corresponding crosscap states.