论文标题
字符串理论，$ \ MATHCAL {N} = 4 $ SYM和RIEMANN假设
String theory, $\mathcal{N}=4$ SYM and Riemann hypothesis
论文作者
论文摘要
我们讨论弦理论，四维$ \ MATHCAL {n} = 4 $超对称Yang-Mills理论（SYM）和Riemann假设之间的新关系。众所周知，Riemann假设等同于Divisors功能之和$σ（n）$的不等式。根据文献的先前结果，我们关注以下事实：$σ（n）$出现在计数$ \ Mathcal {n} = 4 $ sym与$ su（3）$ gauge group的问题中：超级共同索引的schur限制扮演$σ的生成功能。然后，假设Riemann假设给出了$ \ Mathcal {n} = 4 $ sym中$ 1/8 $ -BPS状态的信息的界限。 ADS/CFT对应进一步将Riemann假设与$ ads_5 \ times s^5 $的IIB类超弦理论联系起来。特别是，黎曼假设意味着超级多重型的Kaluza-Klein模式之间的奇迹般的取消，而D3-Branes包裹了弦理论中的超对称循环。我们还讨论了从物理方面获得关于Riemann假设的新见解的可能性。
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 $1/8$-BPS states in the $\mathcal{N}=4$ SYM. The AdS/CFT correspondence further connects the Riemann hypothesis to the type IIB superstring theory on $AdS_5 \times S^5$. In particular, the Riemann hypothesis implies a miraculous cancellation among Kaluza-Klein modes of the supergravity multiplet and D3-branes wrapping supersymmetric cycles in the string theory. We also discuss possibilities to gain new insights on the Riemann hypothesis from the physics side.
