Constructing AdS_2 flow geometries

TL;DR

This paper explores two-dimensional flow geometries in AdS$_2$ spacetimes, linking macroscopic dilaton-gravity models with microscopic SYK-type models, and investigates their thermodynamic and holographic properties.

Contribution

It constructs a precise map between boundary two-point functions and bulk metrics, analyzes constraints from energy conditions, and develops tractable RG flows in SYK models that interpolate between different AdS$_2$ geometries.

Findings

Flow geometries can interpolate between two (near) AdS$_2$ spacetimes.

A map from boundary two-point functions to bulk metrics is established.

RG flows in SYK models are constructed and analyzed at various temperatures.

Abstract

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.