Vacuum stability, string density of states and the Riemann zeta function

TL;DR

This paper explores the deep connection between string theory spectra, vacuum energy, and the zeros of the Riemann zeta function, revealing universal oscillations and implications for the Riemann hypothesis.

Contribution

It establishes a novel link between string spectrum oscillations, vacuum energy, and the zeros of the Riemann zeta function, providing new insights into string stability and number theory.

Findings

Spectrum of excitations exhibits universal oscillations related to zeta zeros

Convergence rate of degrees of freedom to vacuum energy is tied to the Riemann hypothesis

Asymptotic supersymmetry is a necessary condition for stable string vacua

Abstract

We study the distribution of graded degrees of freedom in classically stable oriented closed string vacua and use the Rankin-Selberg transform to link it to the finite one-loop vacuum energy. In particular, we find that the spectrum of physical excitations not only must enjoy asymptotic supersymmetry but actually, at very large mass, bosonic and fermionic states must follow a universal oscillating pattern, whose frequencies are related to the zeros of the Riemann zeta-function. Moreover, the convergence rate of the overall number of the graded degrees of freedom to the value of the vacuum energy is determined by the Riemann hypothesis. We discuss also attempts to obtain constraints in the case of tachyon-free open-string theories.