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$d>2$ Stress-Tensor OPE near a Line
- Source :
- Phys. Rev. D 103, 121702 (2021)
- Publication Year :
- 2021
-
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: $[{\cal L}_m, {\cal L}_n]= (m-n) {\cal L}_{m+n}+ C m (m^2-1) \delta_{m+n,0}$. The dimensionless constant $C$ is proportional to the central charge $C_T$. Transverse integrals in the definition of ${\cal L}_m$ 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 $d=2$ $\cal W$-algebra is observed. This note is motivated by the search for a field-theoretic derivation of $d>2$ correlators in strong coupling critical phenomena.<br />Comment: 15 pages
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. D 103, 121702 (2021)
- Publication Type :
- Report
- Accession number :
- edsarx.2103.09930
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevD.103.L121702