AdS$_2$ Holography: Mind the Cap

TL;DR

This paper constructs new supergravity solutions asymptotic to AdS$_2$, explores their properties, and investigates the implications for the dual CFT$_1$, suggesting it may be dynamical rather than topological.

Contribution

It introduces infinite families of AdS$_2$ solutions with a smooth ten-dimensional cap and analyzes scalar excitations to infer dual CFT$_1$ dynamics.

Findings

Existence of infinite AdS$_2$ supergravity solutions with a smooth cap.

Identification of finite-energy bound states in scalar wave analysis.

Implication that dual CFT$_1$ may be dynamical, not topological.

Abstract

AdS$_2$ plays an extremely important role in black-hole physics. We construct several infinite families of supergravity solutions that are asymptotically AdS$_2$ in the UV, and terminate in the IR with a cap that is singular in two dimensions but smooth in ten dimensions. These solutions break conformal invariance, and should correspond to supersymmetric ground states of a holographically dual CFT$_1$. We solve the free massless scalar wave equation on a family of these solutions, finding towers of finite-energy normalizable bound-state excitations. We discuss the intriguing possibility that these excitations correspond to time-dependent excitations of the dual CFT$_1$, which would imply that this CFT$_1$ is dynamical rather than topological, and hence cannot have a conformally invariant ground state.