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Aspects of electric-magnetic dualities in maximal supergravity

par Lekeu, Victor
Président du jury Argurio, Riccardo
Promoteur Henneaux, Marc
Co-Promoteur Compère, Geoffrey
Publication Non publié, 2018-06-18

Thèse de doctorat

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Résumé :

This thesis is devoted to various aspects of electric-magnetic duality and its gravitational generalization, with an emphasis on the case of maximal supergravity. It is divided into three parts.In the first part, we review the symmetries of maximal supergravity in various dimensions, with a particular focus on the exceptional ``hidden" symmetries that appear upon toroidal dimensional reduction of eleven-dimensional supergravity. Two new results are obtained. First, we prove in detail that these hidden symmetries appear if and only if the Chern-Simons coupling of the eleven-dimensional theory takes the value predicted by supersymmetry. Second, we obtain a manifestly E7(7)-invariant formula for the entropy of non-extremal black holes in four-dimensional N = 8 supergravity.The second part of the thesis concerns the gaugings of extended supergravities in four dimensions. We first show that the embedding tensor formalism does not allow for deformations that cannot be reached by working with the usual Lagrangian in the duality frame picked by the embedding tensor. We then examine through BRST methods the deformations of a large class of non-minimally coupled scalars and abelian vector fields in four dimensions, of which ungauged supergravities offer a prime example. We prove that all local deformations of these models which modify the gauge transformations are of the usual Yang-Mills type, i.e., correspond to the gauging of some rigid symmetries of the undeformed theory. Combined with the first result, this shows that the embedding tensor formalism correctly captures the most general local deformations of these theories.In the third part, we construct self-contained action principles for several types of free fields in six dimensions, whose field strengths satisfy a self-duality condition. These fields are motivated by two considerations. First, their existence allows for a remarkable geometric interpretation of the electric-magnetic duality symmetries of vector fields and linearized gravity in four dimensions. Second, they appear in the spectrum of the chiral N = (4,0) and N = (3,1) ``exotic supergravities" in place of the usual metric. The free action and supersymmetry transformations for those theories are explicitly constructed. We also check that they reduce to linearized maximal supergravity in five dimensions, thus completing the picture of higher-dimensional parents of N = 8 supergravity, at least at the free level. Along the way, we also generalize previous works on linearized supergravity by other authors, in which the graviton and its dual appear on the same footing at the level of the action.We conclude with some open questions, perspectives for future work, and a series of technical appendices.