On Boundary Perturbations in Liouville Theory and Brane Dynamics in Noncritical String Theories

TL;DR

This paper investigates boundary perturbations in Liouville theory and their effects on brane dynamics in noncritical string theories, revealing monodromies, RG flows, and brane decay mechanisms.

Contribution

It provides new insights into boundary monodromies, perturbative RG flows, and exact RG solutions in Liouville theory related to brane dynamics.

Findings

Existence of monodromies in boundary parameters creating Dirichlet admixtures

Perturbative analysis of RG flows related to brane decay

An exactly calculable RG flow acting as a covering transformation

Abstract

We study certain relevant boundary perturbations of Liouville theory and discuss implications of our results for the brane dynamics in noncritical string theories. Our results include (i) There exist monodromies in the parameter $\mu_{\rm B}$ of the Neumann-type boundary condition that create an admixture represented by the Dirichlet type boundary condition. (ii) Certain renormalization group flows can be studied perturbatively, which allows one to determine the results of the corresponding brane decays. (iii) There exists a simple renormalization group flow that can be calculated exactly. In all the cases that we have studied, the RG flow acts like a covering transformation for the mondromies mentioned under (i).