One-loop effective action and the Riemann Zeros

TL;DR

This paper uncovers a surprising link between the distribution of Riemann zeta zeros and the asymptotic behavior of the one-loop effective action in a two-dimensional scalar field theory, exemplified by the non-linear sigma model.

Contribution

It establishes a novel connection between number theory and quantum field theory through the asymptotic analysis of correlation functions and Riemann zeros.

Findings

Fourier transform of two-point functions matches Riemann zero distribution

Explicit example with non-linear sigma model demonstrates the connection

Asymptotic behavior aligns with Riemann zeta function zeros

Abstract

We present a remarkable connection between the asymptotic behavior of the Riemann zeros and one-loop effective action in Euclidean scalar field theory. We show that in a two-dimensional space, the asymptotic behavior of the Fourier transform of two-point correlation functions fits the asymptotic distribution of the non-trivial zeros of the Riemann zeta function. We work out an explicit example, namely the non-linear sigma model in the leading order in $1/N$ expansion.