Flat space holography and complex SYK

TL;DR

This paper explores a novel flat space holographic correspondence in two dimensions, linking a conformally transformed gravity model with a complex SYK model, and derives a boundary action analogous to the Schwarzian.

Contribution

It introduces the first steps towards flat space holography in two dimensions, connecting a specific gravity model with a complex SYK model and deriving a related boundary action.

Findings

Derived a boundary action similar to the Schwarzian

Established a connection between gravity and complex SYK models

Identified a geometric action matching recent discoveries

Abstract

We provide the first steps towards a flat space holographic correspondence in two bulk spacetime dimensions. The gravity side is described by a conformally transformed version of the matterless Callan-Giddings-Harvey-Strominger model. The field theory side follows from the complex Sachdev-Ye-Kitaev model in the limit of large specific heat and vanishing compressibility. We derive the boundary action analogous to the Schwarzian as the key link between gravity and field theory sides and show that it coincides with a geometric action discovered recently by one of us, see 1908.08089.