Rational conformal field theory extensions of W1+∞ in terms of bilocal fields

The rational conformal field theory (RCFT) extensions of W_{1+infinity} atc=1 are in one-to-one correspondence with 1-dimensional integral lattices L(m).Each extension is associated with a pair of oppositely charged ``vertexoperators" of charge square m in N. Their product defines a bilocal fieldV_m(z_1,z_2) whose expansion in powers of z_{12}=z_1-z_2 gives rise to a seriesof (neutral) local quasiprimary fields V^l(z,m) (of dimension l+1). Theassociated bilocal exponential of a normalized current generates theW_{1+infinity} algebra spanned by the V^l(z,1) (and the unit operator). Theextension of this construction to higher (integer) values of the central chargec 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 oforbifold characters, thus extending the range of applications of a recent studyof affine orbifolds.Comment: 16 pages, LaTeX2e (amsfonts), no figure