真空稳定性、弦态密度和黎曼zeta函数
Vacuum stability, string density of states and the Riemann zeta function
摘要：
研究了经典稳定定向闭弦真空中的梯度自由度分布，并利用Rankin-Selberg变换将其与有限单圈真空能量联系起来。特别是，我们发现，频谱的物理激发不仅必须享受渐近超对称性，但实际上，在非常大的质量，玻色子和费米子态必须遵循一个普遍的振荡模式，其频率是有关的黎曼zeta函数的零点。此外，梯度自由度的总数的真空能量的值的收敛速度是由黎曼假设。我们还讨论了在快子自由开放弦论的情况下获得约束的尝试。
英文摘要：
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.
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