General factorization of the n-point beta function into two parts in a möbius-invariant manner

Using the Koba-Nielsen formalism for the generalized beta function, a general form for factorization into two pieces is developed in an entirely Möbius-invariant way. Ward identities for the vertex in the general configuration are derived in a manner which uses only the Möbius invariance of that factor. Special cases (still Möbius-invariant) of this procedure include the multiperipheral, semimultiperipheral, and symmetric factorizations already known.