arXiv subjects

Matteo Cardella

Publications and source records attributed to Matteo Cardella.

4 recordsLinked to original sources

arXiv2010

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

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.

hep-th↗

arXiv2010

Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis

We study asymptotic relations connecting unipotent averages of $Sp(2g,\mathbb{Z})$ automorphic forms to their integrals over the moduli space of principally polarized abelian varieties. We obtain reformulations of the Riemann hypothesis as a class of problems concerning the computation of the equidistribution convergence rate in those asymptotic relations. We discuss applications of our results to closed string amplitudes. Remarkably, the Riemann hypothesis can be rephrased in terms of ultraviolet relations occurring in perturbative closed string theory.

hep-th↗

arXiv2009

A novel method for computing torus amplitudes for $\mathbb{Z}_{N}$ orbifolds without the unfolding technique

A novel method for computing torus amplitudes in orbifold compactifications is suggested. It applies universally for every Abelian $\mathbb{Z}_{N}$ orbifold without requiring the unfolding technique. This method follows from the possibility of obtaining integrals over fundamental domains of every Hecke congruence subgroup $Γ_{0}[N]$ by computing contour integrals over one-dimensional curves uniformly distributed in these domains.

hep-th↗

arXiv2004

Vanishing Perturbative Vacuum Energy in Non-Supersymmetric Orientifolds

We present a novel source for supersymmetry breaking in orientifold models, and show that it gives a vanishing contribution to the vacuum energy at genus zero and three-half. We also argue that all the corresponding perturbative contributions to the vacuum energy from higher-genus Riemann surfaces vanish identically.

hep-th↗