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

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.

1+26 pages, 7 figures. v2 refs added

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Cited by in corpus (6)

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• Species scale, worldsheet CFTs and emergent geometry
• Modular invariance, misalignment and finiteness in non-supersymmetric strings
• On the Running of Gauge Couplings in String Theory
• Tachyons and Misaligned Supersymmetry in Closed String Vacua
• Towards Classification of $\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped $SU(5)$ Asymmetric ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ Heterotic String Orbifolds