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

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

1997-10-16

arxiv.org/abs/hep-th/9710134v1

J.Math.Phys. 39 (1998) 5762-5771

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, LaTeX2e (amsfonts), no figures

Scientific paper

10.1063/1.532591

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.

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