RCFT extensions of W_{1+infinity} in terms of bilocal fields

TL;DR

This paper explores RCFT extensions of W_{1+infinity} at c=1 using bilocal fields, introduces their algebraic structure, extends the framework to higher central charges, and computes characters with chemical potential dependence relevant for quantum Hall systems.

Contribution

It establishes a correspondence between RCFT extensions of W_{1+infinity} and integral lattices, introduces bilocal fields for these extensions, and computes orbifold characters with chemical potential dependence.

Findings

RCFT extensions correspond to 1D integral lattices L(m)

Bilocal fields generate W_{1+infinity} algebra

Characters depend on modular parameter and chemical potential

Abstract

The rational conformal field theory (RCFT) extensions of W_{1+infinity} at c=1 are in one-to-one correspondence with 1-dimensional integral lattices L(m). Each extension is associated with a pair of oppositely charged ``vertex operators" of charge square m in N. Their product defines a bilocal field V_m(z_1,z_2) whose expansion in powers of z_{12}=z_1-z_2 gives rise to a series of (neutral) local quasiprimary fields V^l(z,m) (of dimension l+1). The associated bilocal exponential of a normalized current generates the W_{1+infinity} algebra spanned by the V^l(z,1) (and the unit operator). The extension of this construction to higher (integer) values of the central charge c is also considered. Applications to a quantum Hall system require computing characters (i.e., chiral partition functions) depending not just on the modular parameter tau, but also on a chemical potential zeta. We compute such a zeta dependence of orbifold characters, thus extending the range of applications of a recent study of affine orbifolds.