Notes on Orientifolds of Rational Conformal Field Theories
Ilka Brunner, Kentaro Hori
TL;DR
Brunner and Hori develop a comprehensive framework for constructing crosscap states and parity symmetries in rational conformal field theories, including orbifolds and automorphism twists, with explicit treatment of circle, U(1) rational, gauged WZW, and parafermion systems. They unify Cardy and PSS boundary/crosscap constructions, extend them to orbifolds with discrete torsion, and illuminate geometrical images of A- and B-type parities via mirror symmetry and D-brane configurations. The work provides a concrete dictionary between RCFT data (S, T, P, Y matrices, simple currents) and target-space geometry (orientifold planes, D-branes on circles and disks, parafermion disks), including non-involutive parities and twisted sectors. These results yield practical tools for studying orientifolds in Gepner-type models and more general RCFTs, enabling systematic exploration of parity actions, twisted sectors, and their geometric consequences.
Abstract
We review and develop the construction of crosscap states associated with parity symmetries in rational conformal field theories. A general method to construct crosscap states in abelian orbifold models is presented. It is then applied to rational U(1) and parafermion systems, where in addition we study the geometrical interpretation of the corresponding parities.