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

TL;DR

This paper demonstrates that correlation functions in a free (2k)-form gauge theory on a (4k+2)-dimensional manifold can be factorized into holomorphic and anti-holomorphic parts, linking to chiral (2k)-forms after Wick rotation.

Contribution

It shows the holomorphic factorization of correlation functions in higher-dimensional gauge theories with complex-structured parameters, connecting to chiral forms.

Findings

Correlation functions expressed as sums of holomorphic and anti-holomorphic products.

Holomorphic factors interpreted as chiral (2k)-form correlators.

Establishment of complex structure roles in gauge theory observables.

Abstract

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 observables take their values in spaces with natural complex structures. We show that the correlation functions can be written as a finite sum of terms, each of which is a product of a holomorphic and an anti-holomorphic factor. The holomorphic factors are naturally interpreted as correlation functions for a chiral (2 k)-form, i.e. a (2 k)-form with a self-dual (2 k + 1)-form field strength, after Wick rotation to a Minkowski signature.