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arXiv · 1612.06385

Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators

A. Liam Fitzpatrick·Jared Kaplan·Daliang Li·Junpu Wang
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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.

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A. Liam Fitzpatrick, Jared Kaplan, Daliang Li, Junpu Wang. 2017-09-05. Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators. https://doi.org/10.1007/jhep07(2017)092

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