Non-compact String Backgrounds and Non-rational CFT

TL;DR

This paper introduces microscopic techniques for non-rational conformal field theories, focusing on Liouville theory and the 2D cigar model, to describe strings in non-compact curved backgrounds relevant to dualities and time-dependent processes.

Contribution

It provides a systematic, self-contained overview of methods for non-rational CFTs in non-compact backgrounds, emphasizing Liouville theory and the 2D cigar model.

Findings

Develops techniques for non-rational bulk and boundary CFTs.

Analyzes Liouville field theory and 2D cigar as prototypes.

Facilitates understanding of string dynamics in non-compact backgrounds.

Abstract

This is an introduction to the microscopic techniques of non-rational bulk and boundary conformal field theory which are needed to describe strings moving in non-compact curved backgrounds. The latter arise e.g. in the context of AdS/CFT-like dualities and for studies of time-dependent processes. After a general outline of the central concepts, we focus on two specific but rather prototypical models: Liouville field theory and the 2D cigar. Rather than following the historical path, the presentation attempts to be systematic and self-contained.