On coefficients of operator product expansions for quantum field theories with ordinary, holomorphic, and topological spacetime dimensions

TL;DR

This paper investigates the structure of operator product expansions in quantum field theories with mixed spacetime dimensions, revealing conditions for the appearance of 'derived' functions as coefficients, which generalize classical functions.

Contribution

It provides a comprehensive analysis of 'derived' coefficient functions in OPEs across theories with various spacetime dimensionalities, extending understanding beyond traditional frameworks.

Findings

Identifies conditions for 'derived' functions to appear in OPEs.

Generalizes the concept of raviolo theories to multiple dimensions.

Connects topological, holomorphic, and ordinary spacetime structures in QFTs.

Abstract

In many quantum field theories (such as higher-dimensional holomorphic field theories or raviolo theories), operator product expansions of local operators can have as coefficients not only ordinary functions but also 'derived' functions with nonzero ghost number, which are certain elements of sheaf cohomology. We analyse the 'derived' functions that should appear in operator product expansions for a quantum field theory with an arbitrary number of topological, holomorphic and/or ordinary spacetime dimensions and identify necessary and sufficient conditions for such 'derived' functions to appear. In particular, theories with one topological spacetime dimension and multiple ordinary spacetime dimensions provide a smooth analogue of the (holomorphic) raviolo.