Cosmology Seminar: Gravity as a diffeomorphism invariant gauge theory
Dr Kirill Krasnov, Nottingham University
Wednesday 12 February 2014, 1400-1500
C1 Physics Building
I will explain how Einstein?s General Relativity (with a non-zero cosmological constant) can be reformulated as a dynamical theory of an SU(2) gauge field. The Lagrangian of this formulation is a non-linear function of the curvature, and no other field apart from the connection appears in the action. In particular, there is no metric field. The metric appears in this formulation as being algebraically constructed from the curvature of the connection. The Euler-Lagrange equations following by extermizing this action principle are second order in derivatives. It is then shown that when the connection satisfies its Euler-Lagrange equations the metric constructed from the curvature is Einstein, with non-zero cosmological constant.
To put the above reformulation of GR into wider context, the talk will start with a review of some recent developments in the subject of graviton scattering amplitudes. These developments indicate that, at least on-shell, perturbative gravity is a very simple theory, something that is not at all obvious from examining the perturbative expansion of the Einstein-Hilbert action. One of the motivations for the above reformulation is to exhibit the on-shell simplicity of gravity also off-shell, by providing a better action principle for GR.