36th Meeting of the North British Mathematical Physics Seminar

TBA

We will try to learn a bit about the twistor-string theory of Berkovits & Witten, with particular emphasis on its gravitational degrees of freedom and why these appear to correspond to conformal supergravity. We'll then use an observation of Maldacena to show that one should be able to extract the tree-level S-matrix of Einstein gravity from the twistor-string theory using the equivalence between conformal gravity and general relativity on de Sitter backgrounds. Time permitting, I may talk a bit about how recent formulae for such scattering amplitudes can be understood as arising in this context.

In my talk I will describe a class of theories, dubbed "relative locality theories", being models of interacting relativistic particles with non-trivial geometry of momentum space. I will discuss motivations leading to relative locality; the construction of particles kinematics and dynamics and their relation to the geometry of momentum space; and physical consequences of relaxation of the absolute locality postulate. The fate of relativistic symmetries will be also briefly discussed.

Non-local currents and their associated conserved charges have been known and studied widely in two-dimensional field theories. Their main feature is that their action on product of fields is non-additive i.e. it follows a "deformed" Leibniz rule. Less appreciated is the fact that non-local charges appear in the context of three-dimensional Einstein gravity where they describe the energy-momentum of a "topologically" gravitating point particle. Here momenta are Lorentz group elements and the non-additive action is simply a consequence of the non-abelian structure of the group. After a brief introduction I will show how quantization of such relativistic point particle with group-valued momenta leads to a non-commutative field theory. As an application I will introduce a non-commutative heat-kernel, calculate the associated spectral dimension and comment on its non-trivial behaviour. Finally I will discuss how these structure can be extended to a 4d context and comment on some potential applications.

We present some results of the non-minimal Higgs inflation model and discuss the frame dependence of quantum corrections. Cosmological models with a scalar field non-minimally coupled to gravity are usually formulated in the so called Jordan frame parametrization. It is often useful to perform a field transformation to the so called Einstein frame which formally resem- bles the situation of Einstein Gravity with a minimally coupled scalar field. The action is invariant under field re-parametrizations so that at this level both frames are mathematically equivalent. However, we find that already at the one-loop level this is no longer true since the effective action is not invariant under field reparametrizations. This problem of frame dependence also manifests itself in the scenario of non-minimal Higgs inflation.