In  it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional model in AdS2 ×S1/Z2 with nontrivial boundary conditions in the additional dimension. In this paper we show that a similar picture holds for generalizations of the SYK model with q-fermion interactions. The 3D realization is now given on a space whose metric is conformal to AdS2 × S1/Z2 and is subject to a non-trivial potential in addition to a delta function at the center of the interval. It is shown that a Horava-Witten compactification reproduces the exact SYK spectrum and a non-standard propagator between points which lie at the center of the interval exactly agrees with the bilocal propagator. As q → ∞, the wave function of one of the modes at the center of the interval vanish as 1/q, while the others vanish as 1/q2, in a way consistent with the fact that in the SYK model only one of the modes contributes to the bilocal propagator in this limit.
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Article funded by SCOAP3.
This work of AJ and KS is supported by the Department of Energy under contract DE-SC0010010. The work of KS is also supported by the Galkin Fellowship Award at Brown University. The work of SRD and AG is partially supported by the National Science Foundation grant NSF-PHY-1521045
Das, Sumit R.; Ghosh, Aminik; Jevicki, Antal; and Suzuki, Kenta, "Three Dimensional View of Arbitrary q SYK Models" (2018). Physics and Astronomy Faculty Publications. 596.