Abstract
Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a deformation of the latter. Alternatively, it can be described as an associative quotient of the algebra given by a modified normal ordered product. We clarify the relation of these structures to Zhu's product and Zhu's algebra of the mathematical literature.
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Brungs, D., Nahm, W. The Associative Algebras of Conformal Field Theory. Letters in Mathematical Physics 47, 379–383 (1999). https://doi.org/10.1023/A:1007525300192
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DOI: https://doi.org/10.1023/A:1007525300192