General relativity from $p$-adic strings

Huang, An; Stoica, Bogdan; Yau, Shing-Tung

doi:10.4310/ATMP.2022.v26.n5.a4

General relativity from $p$ -adic strings

An Huang
(
- Harvard U. and
- Brandeis U.
)
,
Bogdan Stoica
(
- Brandeis U. and
- Brown U.
)
,
Shing-Tung Yau
(
- Harvard U.
)

Jan 7, 2019

34 pages

Published in:

Adv.Theor.Math.Phys. 26 (2022) 5, 1203-1237

Published: 2022

e-Print:

1901.02013 [hep-th]

DOI:

10.4310/ATMP.2022.v26.n5.a4

Report number:

BRX-TH-6643,
Brown HET-1778

View in:

ADS Abstract Service

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Citations per year

Abstract: (International Press)

For an arbitrary prime number

p

, we propose an action for bosonic

p

-adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of worldsheet scaling symmetry of the quantum

p

-adic strings, similar to the ordinary bosonic strings case. It turns out that spherical vectors of unramified principal series representations of

PGL (2,\mathbb{Q}_p)

are the plane wave modes of the bosonic fields on

p

-adic strings, and that the regularized normalization of these modes on the padic worldsheet presents peculiar features which reduce part of the computations to familiar setups in quantum field theory, while also exhibiting some new features that make loop diagrams much simpler. Assuming a certain product relation, we also observe that the adelic spectrum of the bosonic string corresponds to the nontrivial zeros of the Riemann Zeta function.

Note:

33 pages, 5 figures

general relativity
p-adic
string model: boson
Einstein equation: vacuum
symmetry: scaling
regularization
zeta function

References(18)

Figures(0)

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General relativity from ppp-adic strings

Citations per year

On ppp-adic string amplitudes in the limit ppp approaches to one