Limits and Degenerations of Unitary Conformal Field Theories

TL;DR

This paper investigates how conformal field theories degenerate and connect to geometric limits, especially analyzing the large level limit of unitary Virasoro minimal models and their geometric interpretations.

Contribution

It introduces a framework for understanding degenerations of CFTs and applies it to analyze the large level limit of unitary Virasoro minimal models.

Findings

Established a notion of convergent sequences of CFTs.

Linked degenerations of CFTs to geometric degenerations.

Analyzed the large level limit of unitary Virasoro minimal models.

Abstract

In the present paper, degeneration phenomena in conformal field theories are studied. For this purpose, a notion of convergent sequences of CFTs is introduced. Properties of the resulting limit structure are used to associate geometric degenerations to degenerating sequences of CFTs, which, as familiar from large volume limits of non-linear sigma models, can be regarded as commutative degenerations of the corresponding ``quantum geometries''. As an application, the large level limit of the A-series of unitary Virasoro minimal models is investigated in detail. In particular, its geometric interpretation is determined.