$d>2$ Stress-Tensor OPE near a Line

Abstract

We study the $TT$ OPE in $d>2$ CFTs 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: $[{\mathcal{L}}_m,{\mathcal{L}}_n]=(m-n){\mathcal{L}}_{m+n}+Cm(m^2-1){\delta }_{m+n,0}$. The dimensionless constant $C$ is proportional to the central charge $C_T$. Transverse integrals in the definition of ${\mathcal{L}}_m$ 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 $d=2$ $\mathcal{W}$-algebra is observed. This note is motivated by the search for a field-theoretic derivation of $d>2$ correlators in strong coupling critical phenomena.

arXiv comment15 pages

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Cited by in corpus (9)

• On the light-ray algebra in conformal field theories
• Symmetry group at future null infinity I: Scalar theory
• On Local and Integrated Stress-Tensor Commutators
• CFT correlators, $\mathcal{W}$-algebras and Generalized Catalan Numbers
• Freedom near Lightcone and ANEC Saturation
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• Toward Null State Equations in $d>2$
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT${}_2$