Entanglement entropy, OTOC and bootstrap in 2D CFTs from Regge and light cone limits of multi-point conformal block

  • Yuya KusukiEmail author
  • Masamichi Miyaji
Open Access
Regular Article - Theoretical Physics


We explore the structures of light cone and Regge limit singularities of n-point Virasoro conformal blocks in c > 1 two-dimensional conformal field theories with no chiral primaries, using fusion matrix approach. These CFTs include not only holographic CFTs dual to classical gravity, but also their full quantum corrections, since this approach allows us to explore full 1/c corrections. As the important applications, we study time dependence of Renyi entropy after a local quench and out-of-time ordered correlator (OTOC) at late time.

We first show that, the n-th (n > 2) Renyi entropy after a local quench in our CFT grows logarithmically at late time, for any c and any conformal dimensions of excited primary. In particular, we find that this behavior is independent of c, contrary to the expectation that the finite c correction fixes the late time Renyi entropy to be constant. We also show that the constant part of the late time Renyi entropy is given by a monodromy matrix.

We also investigate OTOCs by using the monodromy matrix. We first rewrite the monodromy matrix in terms of fusion matrix explicitly. By this expression, we find that the OTOC decays exponentially in time, and the decay rates are divided into three patterns, depending on the dimensions of external operators. We note that our result is valid for any c > 1 and any external operator dimensions. Our monodromy matrix approach can be generalized to the Liouville theory and we show that the Liouville OTOC approaches constant in the late time regime.

We emphasize that, there is a number of other applications of the fusion and the monodromy matrix approaches, such as solving the conformal bootstrap equation. Therefore, it is tempting to believe that the fusion and monodromy matrix approaches provide a key to understanding the AdS/CFT correspondence.


AdS-CFT Correspondence Conformal Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP)Kyoto UniversityKyotoJapan
  2. 2.Department of Physics, Faculty of ScienceThe University of TokyoTokyoJapan

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