Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity - Yuya Kusuki (Journal of High Energy Physics, 2019)
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 general CFT 2 with c > 1. For this purpose, we needed an explicit asymptotic form of the Virasoro conformal blocks in the limit z → 1, which was unknown until now. In this study, we computed it in general by studying the pole structure of the 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 c − 1 12 $$ \frac{c-1}{12} $$ if the total Liouville momentum exceeds beyond the BTZ threshold. This might be interpreted as a black hole formation in AdS3. 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.