Talks

F-theory compactifications on Calabi-Yau fourfolds provide one way to obtain N=1 supersymmetric grand unified models of particle physics from string theory. With this motivation in mind, I will consider F-theory on a particularly simple class of local Calabi-Yau fourfolds, for which a low-energy analysis based upon topological gauge theory is valid. For these models, I will explain how the geometry of the fourfold determines the spectrum of massless charged matter and the effective superpotential in four dimensions. If time permits, I will also discuss the relation between certain surface operators in gauge theory and brane recombination in F-theory.

How sure are you that spacetime is continuous? One of the more radical approaches to quantum gravity, causal set theory, models spacetime as a discrete structure: a causal set. Allowing the possibility that spacetime is discrete then how should we do physics on it? Carrying over the usual continuum descriptions in terms of differential equations seems like a difficult option. This talk begins with a brief introduction to causal sets then describes an approach to modelling the propagation of scalar particles on a causal set. We obtain the continuum causal retarded propagator by summing quantum mechanical amplitudes assigned to paths in the causal set - a kind of \'discrete path integral\' that agrees with the continuum result. The propagator so obtained should serve as a building block towards a model for quantum field theory on a causal set.

The problem of time is studied in a toy model for quantum gravity: Barbour and Bertotti\'s timeless formulation of non-relativistic mechanics. We quantize this timeless theory using path integrals and compare it to the path integral quantization of parameterized Newtonian mechanics, which contains absolute time. In general, we find that the solutions to the timeless theory are energy eigenstates, as predicted by the usual canonical quantization. Nevertheless, the path integral formalism brings new insight as it allows us to precisely determine the difference between the theory with and without time. This difference is found to lie in the form of the constraints imposed on the gauge fixing functions by the boundary conditions. In the stationary phase approximation, the constraints of both theories are equivalent. This suggests that a notion of time can emerge in systems for which the stationary phase approximation is either good or exact. As there are many similarities between this model of classical mechanics and general relativity, these results could provide insight to how time might be emergent in a theory of quantum gravity.

Hawking\'s black hole information paradox is one of the great thought experiments in physics. It points to a breakdown of some central principle of physics, though which one breaks down is still in dispute. It has led to the discovery of ideas that seem to be key to unifying quantum mechanics and gravity, namely the holographic principle and gauge/gravity duality. I review this subject, and discuss ongoing work and future directions.