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A Tale of Two Butterflies: An Exact Equivalence in Higher-Derivative Gravity
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A Tale of Two Butterflies: An Exact Equivalence in Higher-Derivative Gravity
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We prove the equivalence of two holographic computations of the butterfly velocity in higher-derivative theories with Lagrangian built from arbitrary contractions of curvature tensors. The butterfly velocity characterizes the speed at which local perturbations grow in chaotic many-body systems and can be extracted from the out-of-time-order correlator. This leads to a holographic computation in which the butterfly velocity is determined from a localized shockwave on the horizon of a dual black hole. A second holographic computation uses entanglement wedge reconstruction to define a notion of operator size and determines the butterfly velocity from certain extremal surfaces. By direct computation, we show that these two butterfly velocities match precisely in the aforementioned class of gravitational theories. We also present evidence showing that this equivalence holds in all gravitational theories. Along the way, we prove a number of general results on shockwave spacetimes.
Forward citations
Cited by 4 Pith papers
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In TTbar-deformed anomalous CFT2 the chaos bound stays saturated while butterfly velocity depends nontrivially on deformation strength and anomaly, with a Hagedorn regime where the chaotic response turns complex.
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Quantum chaos and pole skipping in two-dimensional conformal perturbation theory
A deformed 2D CFT's stress-tensor pole-skipping point shifts at O(lambda^2); at h=1/2 the shift matches the holographic butterfly velocity.
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