论文标题
标量模块化引导和Riemann Zeta功能的零
Scalar Modular Bootstrap and Zeros of the Riemann Zeta Function
论文作者
论文摘要
使用谐波分析的技术，我们得出了一个交叉方程，该方程仅作用于$ u（1）^c $对称性的任何二维形成共形场理论的标量主要运算符。从这个交叉方程式，我们在所有此类理论的标量差距上得出了界限。相当明显的是，我们的交叉方程包含有关Riemann Zeta函数的所有非平凡零的信息。结果，我们将Riemann假设纯粹是关于在某些二维形成的保形场理论中的标量算子渐近密度的陈述。我们讨论仅使用Virasoro对称性的理论的概括。
Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with $U(1)^c$ symmetry. From this crossing equation, we derive bounds on the scalar gap of all such theories. Rather remarkably, our crossing equation contains information about all nontrivial zeros of the Riemann zeta function. As a result, we rephrase the Riemann hypothesis purely as a statement about the asymptotic density of scalar operators in certain two-dimensional conformal field theories. We discuss generalizations to theories with only Virasoro symmetry.
