Abstract
We search for the extended conformal algebra with two spin-s (s: integer) and one spin-1 generators. This search is inspired by the existence of chiral algebra in the Gaussian model for rational radius. For odd s, the conformal properties of the three-point functions imply that a general fusion rule can be reduced to those of the Gaussian model. For arbitrary even s, these conditions are weaker. In particular, for s=2 we show that the chiral algebra of the Gaussian model is the unique extended conformal algebra with the value of the central charge fixed to be c=1. It is also shown that the conformal generator is necessarily a bilinear of the spin-1 generator just as the Gaussian model. We conjecture that this remains true for arbitrary value of s.
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