added this pointer on the suggestion that the disk worldsheet of the open p-adic string is to be identified with the Bruhat-Tits tree $T_p$:

- Anton Zabrodin,
*Non-Archimedean strings and Bruhat-Tits trees*, Comm. Math. Phys. Volume 123, Number 3 (1989), 463-483 (euclid.cmp/1104178891)

added pointer to today’s

- Paul H. Frampton,
*Particle Theory at Chicago in Late Sixties and p-Adic Strings*(arXiv:2001.10915)

To associate some fog with more fog, I wonder if topological Langlands is about here, relating arithmetic to homotopy theory. I see it gets a mention in Eric Peterson’s new book Formal Geometry and Bordism Operations footnote 18, p. 361.

]]>One thing I haven’t appreciated before is how a Bruhat-Tits building here serves as the disk-shaped worldsheet of the open string.

I have no idea how this relates to taking elliptic curves over arbitrary rings as closed string vacuum diagrams, as it happens in the construction of the string orientation of tmf.

]]>Yes, quite something if some aspect of the Riemann hypothesis emerges from one corner of a “more general number theoretic and homotopy-theoretic refinement of string scattering amplitudes”.

Is there anything deep in mathematics not touched by string/M-theory?

]]>Yes.

It sounds rather striking what they say about Riemann zeta zeros corresponding to the adelic string spectrum. But I haven’t had time yet to try to absorb it.

]]>So this is developing the open bosonic corner you mention in the penultimate paragraph of your MO question?

]]>added more references. Should add some pointer to Bruhat-Tits trees. But no time now.

]]>Preprint today by Yau et al., relating $p$-adic strings to the Riemann zeta function:

- An Huang, Bogdan Stoica, Shing-Tung Yau,
*General relativity from $p$-adic strings*(arXiv:1901.02013)