Sewing Constraints and Non-Orientable Open Strings

TL;DR

This paper extends sewing constraints in Conformal Field Theory to non-orientable surfaces, introducing a new constraint related to the real projective plane, and connects it to open-string spectra.

Contribution

It introduces a novel sewing constraint for non-orientable surfaces and links it to open-string spectral constructions in Conformal Field Theory.

Findings

New sewing constraint for non-orientable surfaces

Connection between the constraint and open-string spectra

Illustration using the real projective plane

Abstract

We extend to non-orientable surfaces previous work on sewing constraints in Conformal Field Theory. A new constraint, related to the real projective plane, is described and is used to illustrate the correspondence with a previous construction of open-string spectra.