Black holes, quantum chaos, and the Riemann hypothesis

从Veneziano到Riemann：黎曼假设的弦论表述

From Veneziano to Riemann: A String Theory Statement of the Riemann Hypothesis

我们讨论了弦论的Veneziano振幅（用黎曼zeta函数的比值改写）与黎曼假设的两个基本判据（用对数的积分和zeta函数的幅角表示）之间的精确关系。我们还讨论了积分准则的基础上的论点的黎曼zeta函数涉及到李准则的黎曼假设。我们提供了一个新的推广这个积分准则。最后，我们评论的物理解释，我们重铸的黎曼假设的Veneziano振幅。

String theory, $\mathcal{N}=4$ SYM and Riemann hypothesis

We discuss new relations among string theory, four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) and the Riemann hypothesis. It is known that the Riemann hypothesis is equivalent to an inequality for the sum of divisors function $σ(n)$. Based on previous results in literature, we focus on the fact that $σ(n)$ appears in a problem of counting supersymmetric states in the $\mathcal{N}=4$ SYM with $SU(3)$ gauge group: the Schur limit of the superconformal index plays a role of a generating function of $σ(n)$. Then assuming the Riemann hypothesis gives bounds on information on…

The Riemann zeros as spectrum and the Riemann hypothesis

We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers. The corresponding Hamiltonian admits a self-adjoint extension that is tuned to the phase of the zeta function, on the critical line, in order to obtain the Riemann zeros as bound states. The model suggests a proof of the Riemann hypothesis in the limit where the potentials vanish. Finally, we propose an interferometer that may yield an experimental observation of the …

Bounds on chaos from the eigenstate thermalization hypothesis

We show that the known bound on the growth rate of the out-of-time-order four-point correlator in chaotic many-body quantum systems follows directly from the general structure of operator matrix elements in systems that obey the eigenstate thermalization hypothesis. This ties together two key paradigms of thermal behavior in isolated many-body quantum systems.

基于本征态热化假说的混沌度量

A measure of chaos from eigenstate thermalization hypothesis

本文提出以本征态热化假说中非对角矩阵元的能量差衰减指数 $γ$ 度量量子混沌，给出 $γ=β/4$ 界限，并通过 SYK 模型与 XXZ 自旋链验证其有效性。

等分布率、闭弦振幅和黎曼假设

Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis

研究了主极化阿贝尔簇的模空间上$Sp(2g,\mathbb{Z})$自守形式的幂单平均与其积分之间的渐近关系。我们得到的黎曼假设的重新作为一类问题的计算等分布收敛速度在这些渐近关系。我们讨论我们的结果的应用程序，以封闭弦振幅。值得注意的是，黎曼假设可以用微扰闭合弦论中的紫外线关系来重新表述。