Bulk equations of motion from CFT correlators

Daniel Kabat; Gilad Lifschytz

doi:10.1007/JHEP09(2015)059

Bulk equations of motion from CFT correlators

Daniel Kabat, Gilad Lifschytz

Department of Physics

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

Abstract

Abstract: To O(1/N) we derive, purely from CFT data, the bulk equations of motion for interacting scalar fields and for scalars coupled to gauge fields and gravity. We first uplift CFT operators to mimic local AdS fields by imposing bulk microcausality. This requires adding an infinite tower of smeared higher-dimension double-trace operators to the CFT definition of a bulk field, with coefficients that we explicitly compute. By summing the contribution of the higher-dimension operators we derive the equations of motion satisfied by these uplifted CFT operators and show that we precisely recover the expected bulk equations of motion. We exhibit the freedom in the CFT construction which corresponds to bulk field redefinitions.

Original language	English
Article number	59
Journal	Journal of High Energy Physics
Volume	2015
Issue number	9
DOIs	https://doi.org/10.1007/JHEP09(2015)059
State	Published - 23 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015, The Author(s).

Keywords

AdS-CFT Correspondence
Models of Quantum Gravity

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1007/JHEP09(2015)059

Cite this

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PY - 2015/9/23

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N2 - Abstract: To O(1/N) we derive, purely from CFT data, the bulk equations of motion for interacting scalar fields and for scalars coupled to gauge fields and gravity. We first uplift CFT operators to mimic local AdS fields by imposing bulk microcausality. This requires adding an infinite tower of smeared higher-dimension double-trace operators to the CFT definition of a bulk field, with coefficients that we explicitly compute. By summing the contribution of the higher-dimension operators we derive the equations of motion satisfied by these uplifted CFT operators and show that we precisely recover the expected bulk equations of motion. We exhibit the freedom in the CFT construction which corresponds to bulk field redefinitions.

AB - Abstract: To O(1/N) we derive, purely from CFT data, the bulk equations of motion for interacting scalar fields and for scalars coupled to gauge fields and gravity. We first uplift CFT operators to mimic local AdS fields by imposing bulk microcausality. This requires adding an infinite tower of smeared higher-dimension double-trace operators to the CFT definition of a bulk field, with coefficients that we explicitly compute. By summing the contribution of the higher-dimension operators we derive the equations of motion satisfied by these uplifted CFT operators and show that we precisely recover the expected bulk equations of motion. We exhibit the freedom in the CFT construction which corresponds to bulk field redefinitions.

KW - AdS-CFT Correspondence

KW - Models of Quantum Gravity

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DO - 10.1007/JHEP09(2015)059

M3 - Article

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SN - 1126-6708

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 9

M1 - 59

ER -

Bulk equations of motion from CFT correlators

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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