Non-critical open strings beyond the semi-classical approximation

TL;DR

This paper investigates quantum corrections to non-critical string theory wave functions using semi-classical Liouville theory, introducing a novel boundary condition that accounts for perimeter constraints and is validated through one-loop calculations.

Contribution

It derives a new boundary condition for Liouville fields in non-critical strings that incorporates perimeter constraints and is compatible with boundary reparametrization invariance.

Findings

Derived a boundary condition involving an exponential integral of the Liouville field.

Computed one-loop corrections to determine an unknown function in the boundary condition.

Enhanced understanding of quantum corrections in non-critical string wave functions.

Abstract

We studied the lowest order quantum corrections to the macroscopic wave functions $\Gamma (A,\ell)$ of non-critical string theory using the semi-classical expansion of Liouville theory. By carefully taking the perimeter constraint into account we obtained a new type of boundary condition for the Liouville field which is compatible with the reparametrization invariance of the boundary and which is not only a mixture of Dirichlet and Neumann types but also involves an integral of an exponential of the Liouville field along the boundary. This condition contains an unknown function of $A/\ell^2$. We determined this function by computing part of the one-loop corrections to $\Gamma (A,\ell)$.