$W_4$ Toda example as hidden Liouville CFT

TL;DR

This paper constructs specific correlators in the $W_4$ Toda conformal field theory and explores their relation to $W_2$ (Virasoro) theory, with implications for 4d conformal theories.

Contribution

It introduces a method to construct correlators in $W_4$ Toda theory and relates them to $W_2$ theory, revealing new connections between these models.

Findings

Constructed $W_4$ Toda correlators for specific representations.

Demonstrated a relation between $W_4$ and $W_2$ theories with different central charges.

Discussed classical limits and their relevance to 4d conformal theories.

Abstract

We construct correlators in the $W_4$ Toda 2d conformal field theory for a particular class of representations and demonstrate a relation to a $W_2$ (Virasoro) theory with different central charge. The relevance of the classical limits of the constructed 3-point functions and braiding matrices to problems in 4d conformal theories is discussed.