Flat Connections for Characters in Irrational Conformal Field Theory

Details Flat Connections for Characters in Irrational Conformal Field Theory Flat Connections for Characters in Irrational Conformal Field Theory

1994-06-13

arxiv.org/abs/hep-th/9406076v1

Int.J.Mod.Phys. A10 (1995) 1181-1218

Physics

High Energy Physics

High Energy Physics - Theory

harvmac (answer b to question) 40 pages. LBL-35718, UCB-PTH-94/15

Scientific paper

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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