1. <math><mi>d</mi><mo>></mo><mn>2</mn></math> stress-tensor operator product expansion near a line
- Author
-
Kuo-Wei Huang
- Subjects
Physics ,Jacobi identity ,010308 nuclear & particles physics ,Cauchy stress tensor ,Critical phenomena ,Field (mathematics) ,01 natural sciences ,symbols.namesake ,0103 physical sciences ,symbols ,Operator product expansion ,Connection (algebraic framework) ,010306 general physics ,Central charge ,Mathematical physics ,Dimensionless quantity - 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.
- Published
- 2021