SYK-like tensor models on the lattice

Abstract

Abstract:We study large N tensor models on the lattice without disorder. We introduce techniques which can be applied to a wide class of models, and illustrate it by studying some specific rank-3 tensor models. In particular, we study Klebanov-Tarnopolsky model on lattice, Gurau-Witten model (by treating it as a tensor model on four sites) and also a new model which interpolates between these two models. In each model, we evaluate various four point functions at large N and strong coupling, and discuss their spectrum and long time behaviors. We find similarities as well as differences from SYK model. We also generalize our analysis to rank-D tensor models where we obtain analogous results as D = 3 case for the four point functions which we computed. For D > 5, we are able to compute the next-to-subleading 1 N corrections for a specific four point function.

Notes on melonic O(N)q−1 tensor models

“…For q ≥ 6 it is not clear that the words above define a unique contraction structure. In case the contraction structure is not unique, we pick one choice -for example the Round-Robin scheduling process to define our interaction [25,26]. 3 The connection between the quantum mechanical theories (1.1) and the SYK model itself is the following; it has been demonstrated (subject to certain caveats) that sum over Feynman graphs of the theory (1.1) coincides with the sum over Feynman graphs of the SYK model at at leading order at large N (see [16] for the argument in a very similar model), even though these two sums differ at finite values of N (see e.g.…”

Towards a finite-N hologram

“…In this paper, we will argue that the holographic tensor models that have recently emerged [26][27][28][29][30][31][32][33][34][35] in the context of SYK models are a potential candidate for such fully solvable theories. See [76][77][78][79][80] for other related works on tensor models.…”

Correlators in the N = 2 $$ \mathcal{N}=2 $$ supersymmetric SYK model

“…The retarded kernel is defined on a complex time contour with two real time folds on two antipodal points on the thermal circle. It can expressed in terms of the retarded and ladder rung propagators 46) which are obtained from the Euclidean propagators by analytic continuation [6,49]. The retarded kernel contributions to the 4-point functions shown in figure 2 are…”

“…The model develops an emergent (approximate) reparametrization symmetry at low energy [6,[17][18][19] that is also present in dilaton gravity theories on AdS 2 [6,[20][21][22][23]. It has intimate relations with wellstudied random matrix models [6,18,[24][25][26][27][28][29][30][31][32], it further boosts the study of a different type of the large-N limit [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], and it is closely related to vector models [49]. The SYK model can be generalized to include extra symmetries [50] or to live in higher dimensions [51][52][53][54][55][56].…”