Liouville Field Theory on an Unoriented Surface

TL;DR

This paper explores Liouville field theory on unoriented surfaces, calculating the one point function on RP^2 and analyzing constraints via crossing symmetry and modular bootstrap.

Contribution

It provides the first calculation of the one point function on RP^2 in Liouville theory and derives constraints using crossing symmetry and modular bootstrap techniques.

Findings

Derived the one point function on RP^2 in Liouville theory.

Identified multiple solutions to the crossing symmetry constraint.

Selected a specific solution through modular bootstrap considerations.

Abstract

Liouville field theory on an unoriented surface is investigated, in particular, the one point function on a RP^2 is calculated. The constraint of the one point function is obtained by using the crossing symmetry of the two point function. There are many solutions of the constraint and we can choose one of them by considering the modular bootstrap.