Subleading Weingartens

Abstract

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.

32 pages + appendices, v2: minor corrections and references

References in corpus (5)

• Black holes as mirrors: quantum information in random subsystems
• JT gravity as a matrix integral
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Efficient decoding for the Hayden-Preskill protocol
• Six-point functions and collisions in the black hole interior

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• Quantum Error Correction from Complexity in Brownian SYK
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• Higher spin JT gravity and a matrix model dual
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• Aspects of Jackiw-Teitelboim Gravity in Anti-de Sitter and de Sitter spacetime