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arXiv 2005.06440hep-thcond-mat.str-elnlin.CD
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Virasoro六点恒等式块与混沌

On the Virasoro six-point identity block and chaos

Tarek Anous, Felix M. Haehl

备注：
29 pages, 5 figures, v2 minor typos fixed, including corrected factors in the definition of $\tilde{T}$. Discussion on the symmetries of the blocks were updated. v3: typos fixed
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摘要：

本文研究了二维共形场论中的六点关联函数，其中六个算子成对地分组，且共形维数相等。假设中心荷$c$很大，频谱很稀疏，对这个关联函数的主要贡献是六点Virasoro恒等块--对应于融合到恒等式及其后代中的每对不同的算子。我们称之为明星频道。在星通道身份块中的一个特定项是应力张量$SL(2,\mathbb{R})$（全局）块，我们推导出一个明确的表达式。在全息背景下，这个物体对应于纯引力中非线性效应的直接测量。我们计算额外的条款，在大$c$作为全球块使用的新理论的重新参数化，这扩展了阴影算子形式主义在一个自然的方式在相同的顺序在大的星通道身份块。我们研究了这些块的相关性的量子混沌的六点扰码的形式在一个时间有序的相关器。有趣的是，全局块不有助于该相关器的加扰模式，这意味着，领先的顺序，六点加扰是不敏感的三点引力子耦合的散装对偶。最后，我们将我们的研究结果与不同的OPE通道，称为梳状通道，并发现在此分解的混沌指数相同的结果。

英文摘要：

We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge $c$ and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block - corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor $SL(2,\mathbb{R})$ (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large $c$ as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks' relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.

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