Kavli Affiliate: Cheng Peng
| First 5 Authors: Cheng Peng, Jia Tian, Yingyu Yang, ,
| Summary:
We study "half-wormhole-like" saddle point contributions to spectral
correlators in a variety of ensemble average models, including various
statistical models, generalized 0d SYK models, 1d Brownian SYK models and an
extension of it. In statistical ensemble models, where more general
distributions of the random variables could be studied in great details, we
find the accuracy of the previously proposed approximation for the
half-wormholes could be improved when the distribution of the random variables
deviate significantly from Gaussian distributions. We propose a modified
approximation scheme of the half-wormhole contributions that also work well in
these more general theories. In various generalized 0d SYK models we identify
new half-wormhole-like saddle point contributions. In the 0d SYK model and 1d
Brownian SYK model, apart from the wormhole and half-wormhole saddles, we find
new non-trivial saddles in the spectral correlators that would potentially give
contributions of the same order as the trivial self-averaging saddles. However
after a careful Lefschetz-thimble analysis we show that these non-trivial
saddles should not be included. We also clarify the difference between "linked
half-wormholes" and "unlinked half-wormholes" in some models.
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