Holographic duals of large-c torus conformal blocks

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.

Section: Virasoro Block From Fusion and Monodromy Approachesmentioning

confidence: 99%

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

Kusuki

Miyaji

2019

“…The global 1-point conformal block on the torus was shown to correspond to the Witten diagram in thermal AdS 3 [22]. In [23,24] the interpretation of the semiclassical n-point conformal block on the torus in terms of geodesics in thermal AdS 3 was suggested.…”

Section: Introductionmentioning

confidence: 99%

Toward the pole

Alekseev

Gorsky

Litvinov

2020

We study the analytic structure of semiclassical conformal blocks, namely of the 1-point conformal block on the torus and of the 4-point conformal block on the sphere, as functions of the intermediate dimension. We interpret their discontinuities, which can be revealed with the use of a particular resummation procedure, holographically in terms of configurations of geodesics in AdS 3 . In other words, we study the behavior of the Ω-deformed N = 2 SYM theory in the Nekrasov-Shatashvili limit near those singular points, where naively the W-boson with non-vanishing angular momentum becomes massless. Upon a proper resummation of instanton contributions, these singularities disappear, which is similar to the Seiberg-Witten solution in the undeformed case where there is no massless W-boson. It is shown that the order parameter undergoes a non-analytic behavior near positions of the poles. The jump of the order parameter is interpreted holographically in terms of geodesic networks.

“…Some other progress attributed to conformal blocks include the study of the dynamics of the Renyi entropy [21,22,1] and out-of-time-ordered correlators (OTOCs) [23]. (See also [24,25,26,27,28,29,30,31,32] for further developments in this direction. ) Although there have been a lot of studies about conformal blocks, we have not reached a perfect understanding of them.…”

Section: Introductionmentioning

confidence: 99%

Large c Virasoro blocks from monodromy method beyond known limits

Kusuki

2018

In this paper, we study large c Virasoro blocks by using the Zamolodchikov monodromy method beyond its known limits. We give an analytic proof of our recent conjecture [1,2], which implied that the asymptotics of the large c conformal blocks can be expressed in very simple forms, even if outside its known limits, namely the semiclassical limit or the heavylight limit. In particular, we analytically discuss the fact that the asymptotic behavior of large c conformal blocks drastically changes when the dimensions of external primary states reach the value c 32 , which is conjectured by our numerical studies. The results presented in this work imply that the general solutions to the Zamolodchikov recursion relation are given by Cardy-like formula, which is an important conclusion that can be numerically drawn from our recent work [1,2]. Mathematical derivations and analytical results imply that, in the bulk, the collision behavior between two heavy particles may undergo a remarkable transition associated with their masses.