Exact Virasoro blocks from Wilson lines and background-independent operators

• Published in: The journal of high energy physics Vol. 2017; no. 7; pp. 1 - 51
• Main Authors: Fitzpatrick, A. Liam, Kaplan, Jared, Li, Daliang, Wang, Junpu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2017; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black holes; Chern-Simons Theories; Classical and Quantum Gravitation; Conformal and W Symmetry; Elementary Particles; Gravity; High energy physics; Kinematics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum gravity; Quantum Physics; Reconstruction; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; Thermodynamics; Wilson, ’t Hooft and Polyakov loops; AdS-CFT Correspondence; Wilson, ’t Hooft and Polyakov loops; Conformal and W Symmetry; Chern-Simons Theories
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2017)092

A bstract Aspects of black hole thermodynamics and information loss can be derived as a consequence of Virasoro symmetry. To bolster the connection between Virasoro conformal blocks and AdS 3 quantum gravity, we study sl(2) Chern-Simons Wilson line networks and revisit the idea that they compute a variety of CFT 2 observables, including Virasoro OPE blocks, exactly. We verify this in the semiclassical large central charge limit and to low orders in a perturbative 1 /c expansion. Wilson lines connecting the boundary to points in the bulk play a natural role in bulk reconstruction. Because quantum gravity in AdS 3 is rigidly fixed by Virasoro symmetry, we argue that sl(2) Wilson lines provide building blocks for background independent bulk reconstruction. In particular, we show explicitly that they automatically ‘know’ about the uniformizing coordinates appropriate to any background state.