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Subleading Weingartens
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Haar integrals over the unitary group contain subleading terms that are needed for unitarity. We study analogous effects in the time evolution operators of JT gravity and Brownian SYK. In JT gravity with bulk matter we find an explanation for the first subleading terms, and in Brownian SYK we find configurations that can explain the full series. An important role is played by slightly off-shell modes that are exponentially amplified by chaos.
Forward citations
Cited by 4 Pith papers
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A de Sitter Anti-Scrambling Algebra
In a toy model of de Sitter quantum gravity, shockwave time advances break the KMS condition and prevent the Hartle-Hawking state from being a trace on the observer's crossed-product algebra.
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The algebraic structure of gravitational scrambling
The paper builds an operator algebra, the modular-twisted product, that captures black hole scrambling exactly at the scrambling time and reduces to previously known free and tensor product algebras in the appropriate limits.
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Negative shocks versus static patch holography
Out-of-time-order correlators along a de Sitter observer worldline, computed with the shockwave eikonal formalism including recoil and backreaction, violate the cyclicity and positivity required of a trace, falsifying...
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Scrambling Enabled Entropy Accumulation in Open Quantum Systems
A weak probe coupled to an open quantum system accumulates a finite Rényi entropy increase only when the system is in the scrambling phase, vanishing in the dissipative phase as the probe coupling goes to zero.
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