# Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity

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## 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 \( \frac{c-1}{12} \) if the total Liouville momentum exceeds beyond the *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.

## Keywords

Conformal Field Theory AdS-CFT Correspondence Field Theories in Lower Dimensions## Notes

### **Open Access**

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