Liouville's Imaginary Shadow

TL;DR

This paper explores a novel bosonization of N=1 super Liouville theory involving an imaginary Liouville field, extending previous proposals and providing detailed checks with potential applications in conformal field theory and related areas.

Contribution

It extends the bosonization of N=1 super Liouville theory to the R sector and offers extensive validation through 3-point function comparisons.

Findings

Successful extension of bosonization to R sector.

Consistent 3-point function comparisons support the proposal.

Potential applications in conformal field theory and gauge theory.

Abstract

N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the OSP(1|2) WZW model. In both setups, the N=1 Liouville field is accompanied by an additional free fermion. Recently, Belavin et al. suggested a bosonization of the product theory in terms of two bosonic Liouville fields. While one of these Liouville fields is standard, the second turns out to be imaginary (or time-like). We extend the proposal to the R sector and perform extensive checks based on detailed comparison of 3-point functions involving several super-conformal primaries and descendants. On the basis of such strong evidence we sketch a number of interesting potential applications of this intriguing bosonization.