Semiclassical Virasoro Blocks from AdS$_3$ Gravity

TL;DR

This paper develops a unified holographic framework using geodesic Witten diagrams and higher spin gauge fields in AdS$_3$ to compute semiclassical Virasoro conformal blocks at large central charge, matching known CFT results.

Contribution

It introduces a bulk construction method for all known semiclassical Virasoro blocks, including an alternative scattering process approach emphasizing their chiral nature.

Findings

Bulk geodesic Witten diagrams reproduce known semiclassical blocks.

An alternative scattering process approach highlights the chiral structure.

Framework can be extended to include corrections and interpolate regimes.

Abstract

We present a unified framework for the holographic computation of Virasoro conformal blocks at large central charge. In particular, we provide bulk constructions that correctly reproduce all semiclassical Virasoro blocks that are known explicitly from conformal field theory computations. The results revolve around the use of geodesic Witten diagrams, recently introduced in arXiv:1508.00501, evaluated in locally AdS$_3$ geometries generated by backreaction of heavy operators. We also provide an alternative computation of the heavy-light semiclassical block -- in which two external operators become parametrically heavy -- as a certain scattering process involving higher spin gauge fields in AdS$_3$; this approach highlights the chiral nature of Virasoro blocks. These techniques may be systematically extended to compute corrections to these blocks and to interpolate amongst the different semiclassical regimes.