Random geometry, quantum gravity and the Kähler potential

Frank Ferrari; Semyon Klevtsov; Steve Zelditch

doi:10.1016/j.physletb.2011.09.098

Random geometry, quantum gravity and the Kähler potential

Frank Ferrari^*, Semyon Klevtsov, Steve Zelditch

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a background-independent measure on the space of metrics can be easily constructed from first principles. Our framework suggests the relevance of a new gravitational effective action and we show that it occurs when coupling the massive scalar field to two-dimensional gravity. This yields new types of quantum gravity models generalizing the standard Liouville case.

Original language	English (US)
Pages (from-to)	375-378
Number of pages	4
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	705
Issue number	4
DOIs	https://doi.org/10.1016/j.physletb.2011.09.098
State	Published - Nov 17 2011

Funding

This work is supported in part by the Belgian FRFC (grant 2.4655.07 ), the Belgian IISN (grant 4.4511.06 and 4.4514.08 ), the IAP Programme (Belgian Science Policy) , the RFBR grant 11-01-00962 and the NSF grant DMS-0904252 .

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.physletb.2011.09.098

Cite this

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title = "Random geometry, quantum gravity and the K{\"a}hler potential",

abstract = "We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a background-independent measure on the space of metrics can be easily constructed from first principles. Our framework suggests the relevance of a new gravitational effective action and we show that it occurs when coupling the massive scalar field to two-dimensional gravity. This yields new types of quantum gravity models generalizing the standard Liouville case.",

author = "Frank Ferrari and Semyon Klevtsov and Steve Zelditch",

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AB - We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a background-independent measure on the space of metrics can be easily constructed from first principles. Our framework suggests the relevance of a new gravitational effective action and we show that it occurs when coupling the massive scalar field to two-dimensional gravity. This yields new types of quantum gravity models generalizing the standard Liouville case.

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Random geometry, quantum gravity and the Kähler potential

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