On the Virasoro six-point identity block and chaos

Abstract

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.

arXiv comment29 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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Cited by in corpus (25)

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• Gaudin Models and Multipoint Conformal Blocks: General Theory
• From Gaudin Integrable Models to $d$-dimensional Multipoint Conformal Blocks
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
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• Six-point functions and collisions in the black hole interior
• Towards Feynman rules for conformal blocks
• Shadow Celestial Amplitude
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• Universal Spinning Casimir Equations and Their Solutions
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• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• Virasoro blocks and the reparametrization formalism
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• Operator growth and black hole formation
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• Conformal Blocks and Bilocal Vertex Operator Transition Amplitudes
• Holographic Black Hole Formation and Scrambling in Time-Ordered Correlators
• Differential equations for classical Virasoro blocks with heavy and light operators