Lightcone commutator and stress-tensor exchange in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>></mml:mo><mml:mn>2</mml:mn></mml:math> conformal field theories
Kuo-Wei Huang
Abstract
Motivated by developing a field-theoretic algebraic approach to the universal part of the stress-tensor sector of a scalar four-point function in a class of higher-dimensional conformal field theories (CFTs), we construct a mode operator, ${\mathcal{L}}_{m}$, near the lightcone in $d=4$ CFTs and show that it leads to a Virasoro-like commutator, including a regularized central-term. As an example, we describe how to reproduce the $d=4$ single-stress tensor exchange contribution in the lightcone limit by a mode summation. A general-$d$ extension is included. We comment on possible generalizations.
Topics & Concepts
CommutatorCauchy stress tensorMathematical physicsScalar (mathematics)Tensor (intrinsic definition)Central chargeConformal mapPhysicsPure mathematicsMathematicsMathematical analysisAlgebra over a fieldGeometryLie conformal algebraBlack Holes and Theoretical PhysicsCosmology and Gravitation TheoriesNumerical methods for differential equations