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

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.

45 pages,13 figures, corrected typos

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• Rademacher Expansions and the Spectrum of 2d CFT
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• Entanglement of Local Operators and the Butterfly Effect
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• Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
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• The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
• Semiclassical Gravity from Averaged Boundaries in two-dimensional BCFTs
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