Quantum corrections to anti-de Sitter space-times: back-reaction from the stress-energy tensor

In this thesis we consider a massless and conformally-coupled scalar field propagating, according to quantum field theory on curved space-time, on three- and four-dimensional anti-de Sitter space. The scalar field is taken to either be static or rigidly-rotating about the polar axis, and is subject to Dirichlet, Neumann or transparent boundary conditions on the anti-de Sitter boundary. Using the framework of Hadamard renormalisation, renormalised stress-energy tensors (QFT-RSETs) are constructed in a thermal state. We also model the quantum scalar field as a classical, thermal gas of noninteracting bosonic particles in the framework of relativistic kinetic theory, constructing macroscopic stress-energy tensors (RKT-SETs). We investigate how well these RKT-SETs approximate the QFT-RSETs by expressing them in terms of four physical quantities: energy density, isotropic pressure, anisotropic pressure and heat flux. The dependence of these on the inverse temperature of the quantum state, the angular speed of rigid rotation and the boundary conditions applied to the field is investigated. We find that at high temperatures, modelling the scalar as a gas of bosonic particles provides a good approximation, but at low temperatures, quantum effects dominate. Within the framework of semi-classical gravity, we then study the back-reaction of the quantum scalar field on anti-de Sitter space-time, using the stress-energy tensors previously constructed. We find that the quantum-corrected geometry is that of massive solitons sourced by the quantum scalar field. The mass of these solitons is investigated, in particular its dependence on the inverse temperature, angular speed and the boundary conditions applied to the field. For linear corrections in three dimensions, the mass is ever-increasing with increasing temperature; for nonlinear corrections in four dimensions, the mass exhibits a limiting value at some temperature, above which the mass decreases. We speculate that this is a manifestation of the breakdown of the semi-classical regime.