c=1 from c<1: Bulk and boundary correlators

TL;DR

This paper investigates the c=1 limit of Liouville theory with FZZT boundary conditions, developing a regularization method to handle divergences and extracting finite, meaningful correlation functions relevant to c=1 string theory.

Contribution

It introduces a regularization procedure for c=1 Liouville theory, clarifies the nature of divergences at the self-dual radius, and provides new results for correlation functions at arbitrary central charge.

Findings

Regularization method for c=1 Liouville correlators

Interpretation of divergences as contact terms

Finite correlation functions after subtraction

Abstract

We study the c_L=25 limit, which corresponds to c=1 string theory, of bulk and boundary correlation functions of Liouville theory with FZZT boundary conditions. This limit is singular and requires a renormalization of vertex operators. We formulate a regularization procedure which allows to extract finite physical results. A particular attention is paid to c=1 string theory compactified at the self-dual radius R=1. In this case, the boundary correlation functions diverge even after the multiplicative renormalization. We show that all infinite contributions can be interpreted as contact terms arising from degenerate world sheet configurations. After their subtraction, one gets a well defined set of correlation functions. We also obtain several new results for correlation functions in Liouville theory at generic central charge.