Tadpole Cancellation in Unoriented Liouville Theory

TL;DR

This paper investigates tadpole cancellation in unoriented Liouville theory using two methods, revealing the necessity of two D1-branes with symplectic gauge group and analyzing differences in finite parts obtained.

Contribution

It compares free field and boundary-crosscap state methods for tadpole cancellation, highlighting their differences and implications in unoriented Liouville theory.

Findings

Two D1-branes with symplectic gauge group cancel tadpole divergences.

Finite parts differ between the two methods and are analyzed.

The validity and applications of the free field method are discussed.

Abstract

The tadpole cancellation in the unoriented Liouville theory is discussed. Using two different methods -- the free field method and the boundary-crosscap state method, we derive one-loop divergences. Both methods require two D1-branes with the symplectic gauge group to cancel the orientifold tadpole divergence. However, the finite part left is different in each method and this difference is studied. We also discuss the validity of the free field method and the possible applications of our result.