Quantum scalar field theory on anti-de Sitter space-time with Robin boundary conditions

In this thesis we study a real quantum scalar field propagating on three (adS3) and four (adS4) dimensional anti-de Sitter space-time with Dirichlet, Neumann and Robin boundary conditions imposed at the space-time boundary. Using Hadamard renormalisation, we numerically compute the vacuum polarisation (VP) on adS3 for a scalar field with general mass and coupling and compare our results with those obtained for the massless, conformally coupled field on adS4. We find that both the vacuum (v.e.v.) and thermal (t.e.v.) expectation values of the VP with Robin boundary conditions converge to the Neumann result at the space-time boundary, except Dirichlet, which has its own limit.

We also numerically compute the v.e.v.s and t.e.v.s of the renormalised stress energy tensor (RSET) for a massless, conformally coupled scalar field on adS4 as well as for the scalar field with general mass and coupling on adS3. Dirichlet, Neumann and Robin boundary conditions are applied at the space-time boundary in both cases. On adS3, we find that with particular values of the coupling constant, we obtain RSETs with negative energy density profiles throughout some or all of the space-time.

Using a selection of the RSETs, obtained for the scalar field with general mass and coupling on adS3, we examine the backreaction of the numerically computed RSETs on the underlying space-time metric. We focus on some of the key features of the quantum-corrected metrics so obtained and make suggestions for future research in this area.