Flat Connections and Non-Local Conserved Quantities in Irrational Conformal Field Theory

Abstract

Irrational conformal field theory (ICFT) includes rational conformal field theory as a small subspace, and the affine-Virasoro Ward identities describe the biconformal correlators of ICFT. We reformulate the Ward identities as an equivalent linear partial differential system with flat connections and new non-local conserved quantities. As examples of the formulation, we solve the system of flat connections for the coset correlators, the correlators of the affine-Sugawara nests and the high-level $n$-point correlators of ICFT.

40 pages, Latex, UCB-PTH-93/33, LBL-34901, CPTH-A277.1293