Constructing AdS2 flow geometries

We consider two-dimensional geometries flowing away from an asymptotically AdS2 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) AdS2 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 AdS2 spacetime and a portion of a dS2 world.