Condensed Matter Seminar: "Thickening and sickening the Sachdev-Ye-Kitaev model"

We discuss higher dimensional generalizations of the 0+1-dimensional Sachdev-Ye-Kitaev (SYK) model. Unlike the previous constructions where multiple SYK copies would be coupled via some spatially short-range one- and/or q-particle random hopping processes, this study focuses on the algebraically varying long-range (spatially and/or temporally) correlated random couplings in d+1 dimensions. Such pertinent topics as translationally-invariant strong-coupling solutions, emergent reparametrization symmetry, effective action for fluctuations, and chaotic behavior (or a lack thereof) are addressed. We find that the most important properties of the original SYK model that make it an appealing example of some potentially exact holographic correspondence do not survive the aforementioned generalizations, thus providing no immediate support for the hypothetical generalized holographic conjecture.