Flat space holography and complex SYK

TL;DR

We develop a flat-space holographic framework in two bulk dimensions by pairing a conformally transformed, matterless CGHS gravity with a complex SYK–like 0+1D boundary theory in the regime of large specific heat and vanishing compressibility. The gravity side yields a boundary action $I^{tw}[h,g]$, the twisted warped analogue of the Schwarzian, arising from both metric and BF formulations and governed by twisted warped conformal symmetries. The field theory side is obtained via a triple scaling limit of complex SYK that sends the effective coupling to infinity while keeping a fixed coupling $\kappa$, reproducing $I^{tw}$ as the dominant boundary action. This work thus provides a concrete route to flat-space holography in 2D and opens avenues to explore chaos, BMS-like structures, and related dilaton-gravity dynamics in flat spacetimes.

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.