Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity

TL;DR

This paper develops a universal light cone bootstrap approach for 2D conformal field theories with c>1, revealing insights into black hole formation, entanglement dynamics, and the Regge limit of conformal blocks.

Contribution

It computes the asymptotic form of Virasoro conformal blocks in the light cone limit and applies it to derive universal results on twist, entanglement, and Regge behavior in 2D CFTs.

Findings

Universal total twist saturated at (c-1)/12 beyond BTZ threshold

Discovery of a Renyi phase transition after a global quench

Universal form of the Regge limit of Virasoro conformal blocks

Abstract

The light cone OPE limit provides a significant amount of information regarding the conformal field theory (CFT), like the high-low temperature limit of the partition function. We started with the light cone bootstrap in the {\it general} CFT ${}_2$ with $c>1$. For this purpose, we needed an explicit asymptotic form of the Virasoro conformal blocks in the limit $z \to 1$, which was unknown until now. In this study, we computed it in general by studying the pole structure of the {\it fusion matrix} (or the crossing kernel). Applying this result to the light cone bootstrap, we obtained the universal total twist (or equivalently, the universal binding energy) of two particles at a large angular momentum. In particular, we found that the total twist is saturated by the value $\frac{c-1}{12}$ if the total Liouville momentum exceeds beyond the {\it BTZ threshold}. This might be interpreted as a black hole formation in AdS${}_3$. As another application of our light cone singularity, we studied the dynamics of entanglement after a global quench and found a Renyi phase transition as the replica number was varied. We also investigated the dynamics of the 2nd Renyi entropy after a local quench. We also provide a universal form of the Regge limit of the Virasoro conformal blocks from the analysis of the light cone singularity. This Regge limit is related to the general $n$-th Renyi entropy after a local quench and out of time ordered correlators.