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Holography principle and arithmetic of algebraic curves

Manin, Yuri I. and Marcolli, Matilde (2002) Holography principle and arithmetic of algebraic curves. . (Submitted)

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According to the holography principle (due to G. ‘t Hooft, L. Susskind, J. Maldacena, et al.), quantum gravity and string theory on certain manifolds with boundary can be studied in terms of a conformal field theory on the boundary. Only a few mathematically exact results corroborating this exciting program are known. In this paper we interpret from this perspective several constructions which arose initially in the arithmetic geometry of algebraic curves. We show that the relation between hyperbolic geometry and Arakelov geometry at arithmetic infinity involves exactly the same geometric data as the Euclidean AdS_3 holography of black holes. Moreover, in the case of Euclidean AdS_2 holography, we present some results on bulk/boundary correspondence where the boundary is a non–commutative space.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:(Submitted on 7 Jan 2002) We are grateful to Alain Connes who suggested the authors to look at [Man2] from the perspective of the holography principle. We also thank Kirill Krasnov for several useful and encouraging comments.
Record Number:CaltechAUTHORS:20170713-074226681
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79054
Deposited By: Ruth Sustaita
Deposited On:13 Jul 2017 16:48
Last Modified:03 Oct 2019 18:15

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