Polynomial equations for rational conformal field theories
Abstract
Duality of the conformal blocks of a rational conformal field theory defines matrices which may be used to construct representations of all monodromies and modular transformations in the theory. These duality matrices satisfy a finite number of independent polynomial equations, which imply constraints on monodromies allowed in rational conformal field theories. The equations include a key identity needed to prove a recent conjecture of Verlinde that the oneloop modular transformation S diagonalizes the fusion rules. Using this formalism we show that duality of the g=0 fourpoint function and modular invariance of all oneloop onepoint functions guarantee modular invariance to all orders. The equations for duality matrices should be useful in the classification of conformal field theories.
 Publication:

Physics Letters B
 Pub Date:
 October 1988
 DOI:
 10.1016/03702693(88)917960
 Bibcode:
 1988PhLB..212..451M