AdS$_{2}$ holography: mind the cap
Résumé
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.