Permutation orientifolds of Gepner models

Abstract

In tensor products of a left-right symmetric CFT, one can define permutation orientifolds by combining orientation reversal with involutive permutation symmetries. We construct the corresponding crosscap states in general rational CFTs and their orbifolds, and study in detail those in products of affine U(1)2 models or N = 2 minimal models. The results are used to construct permutation orientifolds of Gepner models. We list the permutation orientifolds in a few simple Gepner models, and study some of their physical properties -supersymmetry, tension and RR charges. We also study the action of corresponding parity on D-branes, and determine the gauge group on a stack of parity-invariant D-branes. Tadpole cancellation condition and some of its solutions are also presented.

Permutation orientifolds

“…We have checked that this crosscap state leads to consistent one-loop amplitudes, the results can be found in [31]. For a general description of permutation crosscap states on orbifolds see [27].…”

“…Note added: Some of the results of this paper were independently obtained in the paper [27] by Hosomichi.…”

“…We refer to [27] for further discussions of the N = 2 minimal models and their orbifolds. In addition, applications to Gepner models and the construction of string vacua can be found in that paper.…”

“…We do not consider permutation orientifolds of Gepner models, which are however covered in the paper [27].…”

The three-dimensional origin of the classifying algebra

“…These ideas have lead to concrete formulas for operator product coefficients [13,14,15,16,17] with a wide range of uses; see e.g. [18,19,20,21] for some applications in string theory.…”