Higher dimensional generalisations of the SYK model

We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains $N$ Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.Comment: 23 pages, 3 figures. Minor change

SYK/AdS duality with Yang-Baxter deformations

In this paper, based on the notion of SYK/AdS duality we explore the effects of Yang-Baxter (YB) deformations on the SYK spectrum at strong coupling. In the first part of our analysis, we explore the consequences of YB deformations through the Kaluza-Klein (KK) reduction on $(AdS_2)_{\eta}\times (S^1)/Z_2$. It turns out that the YB effects (on the SYK spectrum) starts showing off at \textit{quadratic} order in $1/J$ expansion. For the rest of the analysis, we provide an interpretation for the YB deformations in terms of bi-local/collective field excitations of the SYK model. Using large $N$ techniques, we evaluate the effective action upto quadratic order in the fluctuations and estimate $1/J^2$ corrections to the correlation function at strong coupling.Comment: Revised version, To Appear in JHE