String theory, SYM and Riemann hypothesis
M Honda, T Yoda�- arXiv preprint arXiv:2203.17091, 2022 - arxiv.org
M Honda, T Yoda
arXiv preprint arXiv:2203.17091, 2022•arxiv.orgWe 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 $\sigma
(n) $. Based on previous results in literature, we focus on the fact that $\sigma (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�…
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 $\sigma
(n) $. Based on previous results in literature, we focus on the fact that $\sigma (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�…
We discuss new relations among string theory, four-dimensional 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 . Based on previous results in literature, we focus on the fact that appears in a problem of counting supersymmetric states in the SYM with gauge group: the Schur limit of the superconformal index plays a role of a generating function of . Then assuming the Riemann hypothesis gives bounds on information on the -BPS states in the SYM. The AdS/CFT correspondence further connects the Riemann hypothesis to the type IIB superstring theory on . 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.
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