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arXiv · hep-th/9406076

Flat Connections for Characters in Irrational Conformal Field Theory

M. B. Halpern·N. Sochen
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Abstract

Following the paradigm on the sphere, we begin the study of irrational conformal field theory (ICFT) on the torus. In particular, we find that the affine-Virasoro characters of ICFT satisfy heat-like differential equations with flat connections. As a first example, we solve the system for the general $g/h$ coset construction, obtaining an integral representation for the general coset characters. In a second application, we solve for the high-level characters of the general ICFT on simple $g$, noting a simplification for the subspace of theories which possess a non-trivial symmetry group. Finally, we give a geometric formulation of the system in which the flat connections are generalized Laplacians on the centrally-extended loop group.

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M. B. Halpern, N. Sochen. 1994-06-13. Flat Connections for Characters in Irrational Conformal Field Theory. https://doi.org/10.1142/s0217751x95000565

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