Abstract
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.
Highlights
Introduction & summaryIn this paper we explore asymptotically AdS2 geometries which are generally not isometric to a pure AdS2 geometry in their interior
Working in two-dimensions opens the possibility of obtaining explicit expressions mapping boundary correlation functions to the complete non-linear bulk metric
We are interested in exploring these questions in a setting where the holographic dual is a quantum mechanical theory comprising a finite number of degrees of freedom residing at a sole point on a temporal worldline1 rather than a quantum field theory endowed with spatial locality and a continuous infinity worth of degrees of freedom
Summary
In this paper we explore asymptotically AdS2 geometries which are generally not isometric to a pure AdS2 geometry in their interior. Upon establishing their macroscopic viability, we proceed to build explicit maps from boundary Green functions to detailed features of bulk fields. It seems reasonable to extend the hypothesis of [24,25,26] to the low energy sector of Hdef
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