Fusion rules

{{Short description|Tensor product decomposition rules in representation theory}}

In mathematics and theoretical physics, fusion rules are rules that determine the exact decomposition of the tensor product of two representations of a group into a direct sum of irreducible representations. The term is often used in the context of two-dimensional conformal field theory where the relevant group is generated by the Virasoro algebra, the relevant representations are the conformal families associated with a primary field and the tensor product is realized by operator product expansions. The fusion rules contain the information about the kind of families that appear on the right-hand side of these OPEs, including the multiplicities.

More generally, integrable models in 2 dimensions which aren't conformal field theories are also described by fusion rules for their charges.{{cite journal |arxiv = hep-th/9306162|last1 = Fuchs|first1 = J|title = Fusion rules in conformal field theory|journal = Fortschritte der Physik/Progress of Physics|volume = 42|issue = 1994|pages = 1–48|year = 1994|doi = 10.1002/prop.2190420102|bibcode = 1994ForPh..42....1F| s2cid=14139601 }}