Flat connections for characters in irrational conformal field theory
Jun, 199440 pages
Published in:
- Int.J.Mod.Phys.A 10 (1995) 1181-1218
e-Print:
- hep-th/9406076 [hep-th]
Report number:
- LBL-35718,
- UCB-PTH-94-15
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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 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 , 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.Note:
- harvmac (answer b to question) 40 pages. LBL-35718, UCB-PTH-94/15
- field theory: conformal
- dimension: 2
- space-time: torus
- algebra: Virasoro
- algebra: representation
- differential equations
- group theory: loop space
- coset space
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