Nonperturbative aspects of gravity and field theory

In this thesis we investigate unusual and non-trivial interplays between gravity and field theory. We concentrate on two examples, one related to holography and the other to the physics of false vacuum decay. In the first chapter we overview basic concepts and techniques from both these examples. In chapter 2 we construct solutions describing flows between AdS and Lifshitz spacetimes in IIB supergravity. We find that flows from AdS5 can approach either AdS3 or Lifshitz3 in the IR depending on the values of the deformation from AdS5. Surprisingly, the choice between AdS and Lifshitz in the IR depends only on the value of the deformation, not on its character; the breaking of the Lorentz symmetry in the flows with a Lifshitz IR is spontaneous. We find that the values of the deformation which lead to flows to Lifshitz make the UV field theory dual to the AdS5 geometry unstable, so that these flows do not offer an approach to defining the field theory dual to the Lifshitz spacetime. In chapter 3 we consider the possibility that small black holes can act as nu- cleation seeds for the decay of a metastable vacuum. Using a thin-wall bubble approximation for the nucleation process, we show that black holes can stimulate vacuum decay. In chapter 4 we apply this technique to the particular example of the Higgs potential with generic quantum gravity corrections. We show how small black holes can act as seeds for vacuum decay, spontaneously nucleating a new Higgs phase centred on the black hole with a lifetime measured in millions of Planck times rather than billions of years. The constraints on the parameter space of corrections to the Higgs potential are outlined. We demonstrate that for suitable parameter ranges, the vacuum decay process dominates over the Hawking evaporation process. We also comment on the application of these results to vacuum decay seeded by black holes produced in particle collisions. By relaxing the conditions for the thin-wall approximation and proceeding to the numerical calculations an expansion of the range of the parameter space is proposed