AdS${}_2$ Holography: Mind the Cap

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.

50 pages, 5 figures, v2: typos corrected, reference added

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