E. Verlinde, "Fusion rules and modular transformations in 2D conformal field theory," Nuclear Physics B, 300, 360-76, 27 July 1988.
Erik Verlinde (The Institute for Advanced Study, Princeton, N.J.): "Conformal field theory has received considerable attention because it describes the vacuum solutions of string theory, which is a promising candidate for a consistent quantum theory of all forces in nature. A primary goal is to classify all such vacuum solutions, in the hope that one of them agrees with the observed spectrum of elementary particles and their couplings.
"In this paper a very useful relation is established between two important aspects of conformal field theory. The first is a consistency requirement, known as modular invariance, which severely restricts the allowed spectrum of the theory. The second aspect is the so-called fusion rules, which restrict the allowed couplings. Our result, which is expressed in a simple formula, was a first indication ...
