  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.

High Energy Physics - Theory