Global Conformal Invariance and Bilocal Fields with Rational Correlation Functions

2002/11/12 by Nikolay M. Nikolov, Nikolov, Nikolay M., Yassen S. Stanev +3
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/0211106

13 pages, LATEX, amsfonts, latexsym

arxiv created 2002/12/16 · arxiv updated 2009/11/30

Abstract

The singular part of the operator product expansion (OPE) of a pair of globally conformal invariant (GCI) scalar fields ϕ of (integer) dimension d can be written as a sum of the 2-point function of ϕ and d-1 bilocal conformal fields V_ν(x₁, x₂) of dimension (ν, ν), ν= 1, ..., d-1. As the correlation functions of ϕ(x) are proven to be rational [6], we argue that the correlation functions of V_ν can also be assumed rational. Each V_ν(x₁, x₂) is expanded into local symmetric tensor fields of twist (dimension minus rank) 2ν. The case d=2, considered previously [5], is briefly reviewed and current work on the d=4 case (of a Lagrangean density in 4 space--time dimensions) is previewed.

Related

• Globally conformal invariant gauge field theory with rational correlation functions
• Rationality of Conformally Invariant Local Correlation Functions on Compactified Minkowski Space
• Categorification and correlation functions in conformal field theory
• Revealing the conformal symmetry of the discrete series scalars in dS₂
• Correlation functions of BCFT