Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators

TL;DR

This paper demonstrates that sl(2) Chern-Simons Wilson lines can exactly compute Virasoro conformal blocks and serve as fundamental elements for background-independent bulk reconstruction in AdS$_3$ quantum gravity, especially in the large central charge limit.

Contribution

It establishes a precise connection between Wilson lines and Virasoro blocks, providing a background-independent approach to bulk reconstruction in AdS$_3$ gravity.

Findings

Wilson lines compute Virasoro OPE blocks exactly in the semiclassical limit.

They serve as natural building blocks for background-independent bulk reconstruction.

Wilson lines automatically determine uniformizing coordinates for any background state.

Abstract

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 compute the uniformizing coordinates appropriate to any background state.