One-loop effective action and the Riemann zeros

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 nontrivial zeros of the Riemann zeta function. We work out an explicit example, namely the nonlinear sigma model in the leading order in 1/N expansion.