Constructing AdS2 flow geometries

We consider two-dimensional geometries flowing away from an asymptotically AdS(2) spacetime. Macroscopically, flow geometries and their thermodynamic properties are studied from the perspective of dilaton-gravity models. We present a precise map constructing the fixed background metric from the boundary two-point function of a nearly massless matter field. We analyse constraints on flow geometries, viewed as solutions of dimensionally reduced theories, stemming from energy conditions. Microscopically, we construct computationally tractable RG flows in SYK-type models at vanishing and non-vanishing temperature. For certain regimes of parameter space, the flow geometry holographically encoding the microscopic RG flow is argued to interpolate between two (near) AdS(2) spacetimes. The coupling between matter fields and the dilaton in the putative bulk is also discussed. We speculate on microscopic flows interpolating between an asymptotically AdS(2) spacetime and a portion of a dS(2) world.

Automated summary

The study focuses on the thermodynamic properties of two-dimensional geometries flowing away from an asymptotically AdS(2) spacetime from both macroscopic and microscopic perspectives. A precise map for constructing fixed background metrics and computationally tractable RG flows in SYK-type models at different temperatures is presented. In certain parameter regimes, the flow geometry is argued to interpolate between two (near) AdS(2) spacetimes, suggesting a transition between different spacetime geometries.