Holographic duals of large-c torus conformal blocks

TL;DR

This paper explores the holographic duality between large central charge conformal blocks on a torus in 2D CFT and geodesic networks in thermal AdS space, providing new computational techniques.

Contribution

It establishes a detailed holographic correspondence for large-c torus conformal blocks and develops methods to compute both quantum and classical block functions.

Findings

Classical conformal blocks correspond to geodesic networks in thermal AdS.

Exponentiated global torus blocks approximate classical blocks in certain regimes.

Detailed analysis of the 2-point conformal block and its holographic dual.

Abstract

We study CFT2 conformal blocks on a torus and their holographic realization. The classical conformal blocks arising in the regime where conformal dimensions grow linearly with the large central charge are shown to be holographically dual to the geodesic networks stretched in the thermal AdS bulk space. We discuss the n-point conformal blocks and their duals, the 2-point case is elaborated in full detail. We develop various techniques to calculate both quantum and classical conformal block functions. In particular, we show that exponentiated global torus blocks reproduce classical torus blocks in the specific perturbative regimes of the conformal parameter space.