Orientifolds in N=2 Liouville Theory and its Mirror

TL;DR

This paper studies orientifolds in the N=2 Liouville theory and its mirror, revealing new features and implications for string theory configurations involving black holes, NS5-branes, and gauge theories.

Contribution

It extends previous analyses of orientifolds to the N=2 Liouville and Euclidean black hole models, uncovering novel orientifold properties and their applications.

Findings

Identified new orientifold features in 2D Euclidean black hole models.

Connected orientifold constructions to gauge theories with SO and Sp groups.

Provided examples involving D-branes and O-planes near NS5-branes.

Abstract

We consider unoriented strings in the supersymmetric SL(2,R)/U(1) coset, which describes the two-dimensional Euclidean black hole, and its mirror dual N=2 Liouville theory. We analyze the orientifolds of these theories from several complementary points of view: the parity symmetries of the worldsheet actions, descent from known AdS_3 parities, and the modular bootstrap method (in some cases we can also check our results against known constraints coming from the conformal bootstrap method). Our analysis extends previous work on orientifolds in Liouville theory, the AdS_3 and SU(2) WZW models and minimal models. Compared to these cases, we find that the orientifolds of the two dimensional Euclidean black hole exhibit new intriguing features. Our results are relevant for the study of orientifolds in the neighborhood of NS5-branes and for the engineering of four-dimensional chiral gauge theories and gauge theories with SO and Sp gauge groups with suitable configurations of D-branes and orientifolds. As an illustration, we discuss an example related to a configuration of D4-branes and O4-planes in the presence of two parallel fivebranes.