Analyticity of correlation functions near the positive real axis for general field theory models

Establish the analyticity of correlation functions in a neighborhood of the positive real axis in the complex plane for general field theory models, beyond the special cases (such as the 2D Ising model) where such analyticity has been rigorously proved.

Background

The authors' heuristic explanation of Padé convergence leverages the presumed analyticity of correlation functions near the positive real axis, which supports the use of analytic continuation via rational approximants.

They explicitly note that this analyticity, while widely believed in physics, has not been rigorously established for general field theory models, underscoring a gap in the mathematical foundations relevant to the convergence of Padé-type methods.

References

In particular, the analyticity of correlation function (in our case, G(s) ) in a neighborhood of the positive real axis is a widely held belief but has not been rigorously established for general field theory models except 2D Ising and several other models.

— Strong-coupling expansion and two-point Padé approximation for lattice $φ^4$ field theory  (2604.00525 - Zhu et al., 1 Apr 2026) in Section 3.3.2, "Analytic continuation by Pad e expansion"