Supersymmetric solutions and black hole microstate geometries

2018-07-26In this thesis we investigate different aspects of supersymmetric microstate geometries and construct the renormalization group flows in holographic field theory. The idea of the microstate geometry program is to use the string theory as a consistent theory of quantum gravity to constructively resolve the long-standing black hole information paradox and the related entropy problem by replacing the classical black hole with the horizonless geometry. The microstate geometries are smooth, horizonless solutions of classical supergravity equations which have the same conserved charges as black hole and allow for unitary scattering. There is a hope that one can find enough of them to account for the huge gravitational entropy of black hole at least at the semi-classical level. The construction of such microstates crucially relies on the presence of extra-dimensions, the non-trivial topology of spacetime and the long-ranged supergravity fluxes. ❧ In the first part we consider the supersymmetric renormalization group flows in gauged supergravity which share some of the properties of the black hole microstate geometries such as presence of the large topological cycles threaded by purely magnetic fluxes. The infra-red limit of the solutions appears to be singular from four-dimensional perspective; however, when uplifted to the full eleven-dimensional theory the solutions are remarkably regular. We demonstrate that the physical mechanism underlying this regularity is the same that allows one to resolve black hole singularities in microstate geometries and involves the polarization of M2-branes into M5-branes. We also generalize our flows to a new class of Janus solutions which describe the domain wall defects in the dual holographic field theory. ❧ In the second part we study the properties of the new class of excitations of microstates called W-branes that wrap the topological cycles inside the bubbled microstate geometries. First, we analyze the supersymmetries of the solution that describes the individual W-branes and show that in general it breaks all the supersymmetries of the corresponding black hole and therefore cannot be considered as a microstate. Second, we propose a new approach to supergravity description of W-brane condensates that can encode a large amount of black hole entropy. Our approach is based on extending the bubbled geometry to compactified extra-dimensions and putting them on the same dynamical footing with the spacetime. We find an exact solutions of BPS equations for backgrounds that have the same supersymmetries as the three-charged black hole. ❧ Finally, we examine the tidal forces acting on the radially infalling massive particle in the newly-constructed six-dimensional microstate geometry. These geometries have a long AdS throat that caps-off above the black hole would-be horizon. We find a remarkable difference between how the ordinary matter interacts with microstate compared to its interaction with the classical black hole. We predict that the probe particle must undergo highly energetic stringy transition before it reaches the cap of the geometry, and thus particle will ultimately scramble into microstate geometry