Dimensional continuation without perturbation theory

TL;DR

The paper introduces a non-perturbative formula for extending physical correlation functions to fractional dimensions, which aligns with known perturbative results at one loop.

Contribution

It presents a novel, perturbation-independent method for dimensional continuation of correlation functions using infinite weighted sums.

Findings

The formula reproduces correct weak coupling dimension dependence at one loop.

It is motivated by strong coupling expansion but does not rely on perturbation theory.

The approach generalizes dimensional continuation beyond traditional perturbative methods.

Abstract

A formula is proposed for continuing physical correlation functions to non-integer numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is motivated by studying the strong coupling expansion, but the end result makes no reference to any perturbation theory. It is shown that the formula leads to the correct dimension dependence in weak coupling perturbation theory at one loop.