Subleading Weingartens
Douglas Stanford, Zhenbin Yang, and Shunyu Yao
TL;DR
This paper investigates subleading effects in Haar integrals and their analogs in quantum gravity and SYK models, revealing how off-shell modes and chaos influence unitarity and series expansions.
Contribution
It provides a new explanation for subleading terms in JT gravity with matter and full series understanding in Brownian SYK, highlighting the role of off-shell modes.
Findings
Subleading Haar integral terms are explained in JT gravity with matter.
Full series of effects in Brownian SYK are characterized.
Off-shell modes exponentially amplified by chaos are crucial.
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.
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