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.

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

References in corpus (8)

• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Disrupting Entanglement of Black Holes
• Holographic dual of the five-point conformal block
• Phases of scrambling in eigenstates
• Thermal out-of-time-order correlators, KMS relations, and spectral functions
• From Conformal Blocks to Path Integrals in the Vaidya Geometry
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Holographic Description of 2D Conformal Block in Semi-classical Limit

Cited by in corpus (25)

• OPE statistics from higher-point crossing
• 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
• Recursion relations for 5-point conformal blocks
• Seven-Point Conformal Blocks in the Extended Snowflake Channel and Beyond
• Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation
• Toward random tensor networks and holographic codes in CFT
• Six-point functions and collisions in the black hole interior
• Towards Feynman rules for conformal blocks
• Shadow Celestial Amplitude
• Feynman Rules for Scalar Conformal Blocks
• More on Wilson toroidal networks and torus blocks
• Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges
• Universal Spinning Casimir Equations and Their Solutions
• Lightcone Modular Bootstrap and Tauberian Theory: A Cardy-like Formula for Near-extremal Black Holes
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• Virasoro blocks and the reparametrization formalism
• Toward Null State Equations in $d>2$
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Operator growth and black hole formation
• Holography for bulk states in 3D quantum gravity
• 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