Generalisations of the Sachdev-Ye-Kitaev model

The Sachdev-Ye-Kitaev model has recently sparked a lot of interest in the research community due to its peculiar properties: it is solvable at strong coupling, where it exhibits a conformal symmetry and it saturates the chaos bound, in fact it is holographically dual to a black hole in AdS space. The model consists in a set of large N Majorana fermions in 0+1 dimensions with an all-to-all random interaction. We review the main properties of the model and some of the many variants and generalizations that have been proposed, highlighting the characteristics which makes it possible to maintain the same behaviour. We also study next-to-leading order corrections both in the number of degrees of freedom and in the disorder of the couplings.