MHV leaf amplitudes from parafermions

TL;DR

This paper presents a dual conformal field theory (CFT) framework for MHV leaf amplitudes using non-compact parafermions and affine Kac-Moody currents, connecting it with existing Liouville-based models.

Contribution

It introduces a new CFT representation of MHV leaf amplitudes involving parafermions, aligning with and extending previous Liouville-based approaches.

Findings

Consistent dual CFT description of MHV leaf amplitudes.

Establishes equivalence via $H_3^+$ WZW-Liouville correspondence.

Links parafermion approach with existing Liouville models.

Abstract

We give a dual CFT representation of MHV leaf amplitudes in the large $N$ and semiclassical limit in terms of non-compact parafermions and a single affine Kac-Moody current for $SO(N)$. This representation is consistent with the other 2D CFT realization of 4D leaf amplitudes proposed in the literature, which is based on a dressed Liouville theory. The equivalence between the two CFT descriptions arises from the $H_3^+$ WZW-Liouville correspondence, applied to the $SL(2,\mathbb{R})/U(1)$ coset theory in the spectrally flowed sector.