Quantum Black Holes: Some static and dynamical aspects

Abstract

With the aim of understanding single-center black hole entropy in \mathcal{N}=2 compactifications in string theory, we study the lowest lying states in the dual conformal field theories. We analyse the low-lying spectrum to isolate all possible contributions to the partition function in the regime where no single-center black holes contribute; this is the strictly polar regime of moduli-space where the single-center cosmic censorship bound is violated. These contributions uniquely determine the entire partition function. This analysis paves a clear path for pushing into the non-polar sector to subtract away all multi-center contributions to be left with the single-center degeneracies. To study near-extremal black holes, with a view towards dynamics, within a controlled string theoretic setting, we use Scherk-Schwarz compactifications to break supersymmetry. We show that the leading order entropy of these near-extremal black holes in gauged supergravity are correctly reproduced by dual conformal field theories realizing the \rho-algebras of Schwimmer and Seiberg. To further study dynamical aspects of black holes, we study the dynamics associated to the Schwarzschild black hole horizon. We show that the degrees of freedom associated to 't Hooft's black hole S-Matrix can be reformulated in terms of a collection of inverted harmonic oscillators; this allows us to write down the corresponding Hamiltonian of evolution explicitly. Furthermore, we identify a connection to 2d string theory which in turn allows us to show that there is an exponential degeneracy of how a given total initial energy may be distributed among many partial waves of the 4d black hole; much as is expected from the growth of states associated to black hole entropy. Finally, to elucidate the structure of hard-soft couplings in QCD (like) theories, we show how the requirement that there exists a local and conserved energy-momentum tensor constrains the effective parameters and semi-holographic coupling between the perturbative and the non-perturbative sectors. Thus we realize a concrete democratic formulation of semi-holography at arbitrary energy scales. We illustrate the construction of semi-holography with a bi-holographic toy model in which the perturbative UV dynamics of semi-holography will be replaced by a strongly coupled holographic theory that admits a classical gravity description on its own. The infrared sector will be even more strongly coupled and also holographic. We explicitly demonstrate that simple consistency conditions can determine the hard-soft couplings between the two sectors and the parameters of the IR theory as functions of the parameters of the UV theory. Furthermore, the behavior of the hard-soft couplings in the UV is state-independent and can be obtained from the construction of the vacuum state. However, the running of the hard-soft couplings with the scale is state-dependent. The parameters defining the holographic IR classical gravity theory are fixed by the vacuum state of the full theory while the gravitational fields undergo state-dependent field re-definitions in excited states.