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We consider a free (2 k)-form gauge-field on a Euclidean (4 k + 2)-manifold.The parameters needed to specify the action and the gauge-invariant observablestake their values in spaces with natural complex structures. We show that thecorrelation functions can be written as a finite sum of terms, each of which isa product of a holomorphic and an anti-holomorphic factor. The holomorphicfactors are naturally interpreted as correlation functions for a chiral (2k)-form, i.e. a (2 k)-form with a self-dual (2 k + 1)-form field strength,after Wick rotation to a Minkowski signature.Comment: 11 pages. Late

Holomorphic factorization of correlation functions in (4k+2)-dimensional (2k)-form gauge theory