Constraints on Symmetries from Holography.

Daniel Harlow,Hirosi Ooguri

doi:10.1103/physrevlett.122.191601

Abstract

In this Letter we show that a set of old conjectures about symmetries in quantum gravity hold within the anti-de Sitter/conformal field theory correspondence. These conjectures are that no global symmetries are possible, that internal gauge symmetries must come with dynamical objects that transform in all irreducible representations, and that internal gauge groups must be compact. These conjectures are not obviously true from a bulk perspective, they are nontrivial consequences of the nonperturbative consistency of the correspondence. More details of and background for these arguments are presented in an accompanying paper.

Highlights

In this Letter we show that a set of old conjectures about symmetries in quantum gravity hold within the anti–de Sitter/conformal field theory correspondence
These conjectures are that no global symmetries are possible, that internal gauge symmetries must come with dynamical objects that transform in all irreducible representations, and that internal gauge groups must be compact
Introduction.—There is an old set of conjectural constraints on symmetries in quantum gravity [1,2,3]: (i) Quantum gravity does not allow global symmetries. (ii) Quantum gravity requires that there must be dynamical objects transforming in all irreducible representations of any internal gauge symmetry. (iii) Quantum gravity requires that any internal gauge symmetry group is compact

Summary

Constraints on Symmetries from Holography

In this Letter we show that a set of old conjectures about symmetries in quantum gravity hold within the anti–de Sitter/conformal field theory correspondence These conjectures are that no global symmetries are possible, that internal gauge symmetries must come with dynamical objects that transform in all irreducible representations, and that internal gauge groups must be compact. None of these conjectures is true as a statement about classical Lagrangians, e.g., the shift symmetry of a free massless scalar field coupled to Einstein gravity violates conjectures (i) and (iii), and the gauge invariance of pure Maxwell theory coupled to Einstein gravity violates conjecture (ii) Any argument for these conjectures must rely on properties of nonperturbative quantum gravity. Given a spatial subregion R of the boundary CFT, a codimension-two bulk surface γR is a Hubeny-RangamaniTakayanagi (HRT) surface for R if (a) we have ∂γR 1⁄4 ∂R, (b) the area of γR is extremal under variations of its location which preserve ∂γR, (c) there exists an achronal codimension-one bulk surface HR such that ∂HR 1⁄4 γR ∪ R, and

Published by the American Physical Society

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