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  • Letter
  • Open Access

d>2 stress-tensor operator product expansion near a line

Kuo-Wei Huang

  • Department of Physics, Boston University, Commonwealth Avenue, Boston, Massachusetts 02215, USA

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Phys. Rev. D 103, L121702 – Published 10 June, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.L121702

Abstract

We study the operator product expansion of stress tensors (TT OPE) in d>2 conformal field theories whose bulk dual is Einstein gravity. Directly from the TT OPE, we obtain, in a certain null-like limit, an algebraic structure consistent with the Jacobi identity: [Lm,Ln]=(m−n)Lm+n+Cm(m2−1)δm+n,0. The dimensionless constant C is proportional to the central charge CT. Transverse integrals in the definition of Lm play a crucial role. We comment on the corresponding limiting procedure and point out a curiosity related to the central term. A connection between the d>2 near-lightcone stress-tensor conformal block and the d=2 W algebra is observed. This note is motivated by the search for a field-theoretic derivation of d>2 correlators in strong coupling critical phenomena.

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Phys. Rev. D 103, L121702– Published 10 June, 2021
  • Received 1 April 2021
  • Accepted 21 May 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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