On the stress tensor light-ray operator algebra

2020/11/30 by Alexandre Belin, Diego M. Hofman, Grégoire Mathys +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebra over a field #Black Holes and Theoretical Physics #Cauchy stress tensor #Central charge #Conformal field theory #Conformal map #Geometry #Integrable system #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Operator algebra #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Subalgebra #hep-th

paper · pdf · doi:10.1007/jhep05(2021)033

published in Journal of High Energy Physics 2021(5) (Springer Nature) · 56 pages + appendices, 9 figures; published version

arxiv created 2021/03/11 · openalex publication_date 2021/05/05 · arxiv updated 2021/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A bstract We study correlation functions involving generalized ANEC operators of the form ∫ dx^-(x^-)ⁿ⁺²T_--(\overrightarrowx) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∫</mml:mo> <mml:msup> <mml:mi>dx</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:msup> <mml:mfenced> <mml:msup> <mml:mi>x</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:mfenced> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mo>−</mml:mo> </mml:mrow> </mml:msub> <mml:mfenced> <mml:mover> <mml:mi>x</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:mfenced> </mml:math> in four dimensions. We compute two, three, and four-point functions involving external scalar states in both free and holographic Conformal Field Theories. From this information, we extract the algebra of these light-ray operators. We find a global subalgebra spanned by n = − 2 , − 1 , 0 , 1 , 2 which annihilate the conformally invariant vacuum and transform among themselves under the action of the collinear conformal group that preserves the light-ray. Operators outside this range give rise to an infinite central term, in agreement with previous suggestions in the literature. In free theories, even some of the operators inside the global subalgebra fail to commute when placed at spacelike separation on the same null-plane. This lack of commutativity is not integrable, presenting an obstruction to the construction of a well defined light-ray algebra at coincident \overrightarrowx <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>x</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:math> coordinates. For holographic CFTs the behavior worsens and operators with n ≠ − 2 fail to commute at spacelike separation. We reproduce this result in the bulk of AdS where we present new exact shockwave solutions dual to the insertions of these (exponentiated) operators on the boundary.

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