Virasoro Symmetry in a 2h-dimensional Model and Its Implications

TL;DR

This paper explores a 2h-dimensional generalization of the Coulomb gas model, revealing that certain hypergeometric functions satisfy null vector decoupling relations linked to Virasoro algebra, with implications for conformal field theory.

Contribution

It introduces a novel 2h-dimensional Coulomb gas model where hypergeometric functions relate to Virasoro algebra via null vector decoupling.

Findings

Hypergeometric functions satisfy null vector relations

Virasoro algebra structure emerges in higher dimensions

Connections to conformal field theory established

Abstract

The set of two partial differential equations for the Appell hypergeometric function in two variables F_4(a,b,c,a+b-c+2-h,x,y) is shown to arise as a null vector decoupling relation in a 2h-dimensional generalisation of the Coulomb gas model. It corresponds to a level two singular vector of an intrinsic Virasoro algebra.