An exact operator that knows its location

• Published in: The journal of high energy physics Vol. 2018; no. 2; pp. 1 - 49
• Main Authors: Anand, N., Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, Li, Daliang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: 1/N Expansion; AdS-CFT Correspondence; Classical and Quantum Gravitation; Conformal and W Symmetry; Conformal Field Theory; Correlators; Elementary Particles; Gravitation theory; High energy physics; Perturbation theory; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; AdS-CFT Correspondence; Conformal and W Symmetry; Conformal Field Theory; 1/N Expansion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2018)012

A bstract We use conformal symmetry to define an AdS 3 proto-field ϕ as an exact linear combination of Virasoro descendants of a CFT 2 primary operator O . We find that both symmetry considerations and a gravitational Wilson line formalism lead to the same results. The operator ϕ has many desirable properties; in particular it has correlators that agree with gravitational perturbation theory when expanded at large c , and that automatically take the correct form in all vacuum AdS 3 geometries, including BTZ black hole backgrounds. In the future it should be possible to use ϕ to probe bulk locality and black hole horizons at a non-perturbative level.