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Notes on the SYK model in real time

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arxiv 1801.08118 v1 pith:52HGOMMX submitted 2018-01-24 hep-th

Irina Aref'eva , Igor Volovich This is my paper · ORCID
classification hep-th
keywords modeltimebilocaldefinedfieldsfunctionalnonperturbativereal
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Nonperturbative formulation of the Sachdev-Ye-Kitaev (SYK) model is discussed. The partition function of the model can be represented as a functional integral over the Grassmann variables in Euclidean time which is well defined but it diverges after the transformation to the fermion bilocal fields. We point out that the generating functional of the SYK model in real time is well defined even after the transformation to the bilocal fields and it can be used for nonperturbative investigations of its properties. The SYK model in zero dimensions is studied, its large N expansion is evaluated and phase transitions are investigated.

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  1. Schwarzian functional integrals calculus

    hep-th 2019-08 conditional novelty 6.0 of 10

    Schwarzian functional integrals over Diff^1_+(S^1)/SL(2,R) are reduced to ordinary integrals, giving two- and four-point correlators that do not factorize into two-point products.

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