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Magnetic charges and phase space renormalization of gravity



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Tomova, Bilyana 


In the first part of this thesis we perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions – those that are analytic near I+ – admit a non-trivial action of the generalised Bondi-Metzner-van der Burg- Sachs (GBMS) group which contains infinite-dimensional supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff×Weyl transformations of the celestial S4. Using the covariant phase space formalism and a new technique which we present in this thesis (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are local and covariant. The Hamiltonian charges corresponding to GBMS diffeomorphisms are non-integrable. We show that the integrable part of these charges faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of infinite-dimensional asymptotic symmetries in higher even dimensional non-linear gravity.

In the second part of this thesis, we study the dual charges of N = 1 supergravity in asymptotically flat spacetime. The action considered is the usual supergravity action with a topological contribution. This is the Nieh-Yan term and the magnetic term of the free Rarita-Schwinger field. Through methods of the covariant phase space formalism we construct the charges conjugate to supersymmetry, diffeomorphism and Lorentz transformations. The additional term in the action will lead to new, non-vanishing contributions to these charges. The magnetic diffeomorphism charges are equivalent to the ones previously found for gravity, while the dual supersymmetric charges are new and do not appear for the free Rarita-Schwinger field. We find that the asymptotic symmetry group for supergravity can only include global conformal transformations on the celestial sphere.





Perry, Malcolm


asymptotic symmetries, gravity


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
Science and Technology Facilities Council (2520200)