AdS(2) black holes and soliton moduli spaces

An AdS₂ black hole spacetime is an AdS₂ spacetime together with a preferred choice of time. The Boulware, Hartle-Hawking and SL(2, $R$) invariant vacua are constructed, together with their Green functions and stress tensors, for both massive and massless scalars in an AdS₂ black hole. The classical Bekenstein-Hawking entropy is found to be independent of the temperature, but at one loop a non-zero entanglement entropy arises. This represents a logarithmic violation of finite-temperature decoupling for AdS₂ black holes which arise in the near-horizon limit of an asymptotically flat black hole. Correlation functions of the boundary conformal quantum mechanics are computed as functions of the choice of AdS ₂ vacuum.; The Kaluza-Klein spectrum of $N$ = 2, D = 4 supergravity compactified on AdS ₂ × S2 is found and shown to consist of two infinite towers of SU(1, 1|2) representations. In addition to ‘pure gauge’ modes living on the boundary of AdS ₂ which are familiar from higher dimensional cases, in two dimensions there are modes (e.g. massive gravitons) which enjoy no gauge symmetry yet nevertheless have no on-shell degrees of freedom in the bulk. These subtleties are discussed in detail.; Quantum mechanics on the moduli space of N supersymmetric Reissner-Nordstrom black holes is shown to admit 4 supersymmetries using an unconventional supermultiplet which contains 3N bosons and 4N fermions. A near-horizon limit is found in which the quantum mechanics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This near-horizon theory is shown to have enhanced D(2, 1; 0) superconformal symmetry, which includes an SU (2) × SU(2) R-symmetry arising from spatial rotations and the R-symmetry of $N$ = 2 supergravity.; The final chapter of this thesis applies moduli space techniques to the study of multi-solitons in noncommutative scalar field theories at large &thetas; in arbitrary dimension. In two spatial dimensions, the parameter space for k solitons, is a Kähler de-singularization of the symmetric product ($R2$)k/S_k. In four dimensions the moduli space provides an explicit Kähler resolution of ($R4$)k/S_k. In general spatial dimension, 2d, it is isomorphic to the Hilbert scheme of k points in $Cd$, which for d > 2 (and k > 3) is not smooth and can have multiple branches.