Low energy quantum gravity

Abstract

This thesis investigates two very di erent aspects of quantum gravity. In the rst - and main - section, we examine the question of quantum gravitational contributions to the running of a coupling parameter alongside the various problems and issues that this raises. We treat quantum gravity as an e ective eld theory and use perturbative methods to address issues. Speci cally, we look at a '4-type scalar coupling. In a gauge-invariant way, we consider a non-minimally coupled, massive scalar eld, with non-constant background, in the presence of a cosmological constant and contrary to most of the literature, we also calculate all derivative terms. An e ective action is constructed, renormalization counterterms calculated, and we nd that, within certain bounds, gravity leads to asymptotic freedom of scalar eld theory. Furthermore, we investigate whether considering quadratic divergences in gravitational calculations can tell us anything useful. In this case we nd non-vanishing quadratic divergences. However, we also recognise the possibility that quadratic divergences are somewhat of a red herring and that by suitable eld rede nitions, we can eliminate these from our calculations. The second section of the thesis addresses the possibility of super uidity in a quark gluon plasma. We use the framework of AdS/CFT, with knowledge of black hole thermodynamics, to consider the duality between a black hole in anti-de Sitter space and a uid existing on the boundary. Initially, we look at a simple case of a black hole possessing only mass and charge in AdS spacetime and calculate such properties as the entropy, temperature and speci c heat capacity, identifying a telltale sign of a phase change (speci c heat capacity tending to in nity) and of points of vanishing viscosity (corresponding with a zero entropy). After con rming that such a boundary exists, we take a di erent approach where we calculate and interpret the solutions to a relativistic Gross-Pitaevskii equation on a sphere. On projection back to R3, the solutions are seen to be tori, which we choose to interpret as vortex rings in analogy to the expected feature of those which are known to appear in a real super uids.