# Thickening and sickening the SYK model

## TL;DR

This paper explores higher-dimensional generalizations of the SYK model with long-range correlated couplings, revealing that key properties supporting holographic duality in the original model do not persist.

## Contribution

It introduces a new class of SYK generalizations with algebraically varying long-range couplings and analyzes their physical properties and limitations.

## Key findings

- Original SYK properties do not survive in the generalized models
- Lack of evidence for holographic duality in the generalized models
- Long-range couplings alter key features like reparametrization symmetry

## Abstract

We discuss higher dimensional generalizations of the 0+1-dimensional Sachdev-Ye-Kitaev (SYK) model that has recently become the focus of intensive interdisciplinary studies by, both, the condensed matter and field-theoretical communities. Unlike the previous constructions where multiple SYK copies would be coupled to each other and/or hybridized with itinerant fermions via spatially short-ranged random hopping processes, we study algebraically varying long-range (spatially and/or temporally) correlated random couplings in the general d+1 dimensions. Such pertinent topics as translationally-invariant strong-coupling solutions, emergent reparametrization symmetry, effective action for fluctuations, chaotic behavior, and diffusive transport (or a lack thereof) are all addressed. We find that the most appealing properties of the original SYK model that suggest the existence of its 1+1-dimensional holographic gravity dual do not survive the aforementioned generalizations, thus lending no additional support to the hypothetical broad (including 'non-AdS/non-CFT') holographic correspondence.