The Mini-Superspace Limit of the SL(2,C)/SU(2)-WZNW Model

TL;DR

This paper analyzes the mini-superspace limit of the SL(2,C)/SU(2)-WZNW model, revealing insights into its spectrum, structure, and correlation functions by harmonic analysis, simplifying the understanding of noncompact coset models.

Contribution

It provides a detailed formulation of the mini-superspace limit as baby-CFT for the SL(2,C)/SU(2) model, including spectrum, structure constants, and fusion rules, using harmonic analysis.

Findings

Spectrum and structure constants derived from harmonic analysis.

Fusion rules and four-point function factorization established.

Clarifies operator-state correspondence and non-normalizable states.

Abstract

Many qualitatively new features of WZNW models associated to noncompact cosets are due to zero modes with continuous spectrum. Insight may be gained by reducing the theory to its zero-mode sector, the mini-superspace limit. This will be discussed in some detail for the example of SL(2,C)/SU(2)-WZNW model. The mini-superspace limit of this model can be formulated as baby-CFT. Spectrum, structure constants and fusion rules as well as factorization of four point functions are obtained from the harmonic analysis on SL(2,C)/SU(2). The issues of operator-state correspondence or the appearance of non-normalizable intermediate states in correlation functions can be discussed transparently in this context.