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Title: Supergravity in superspace : supergeometry, differential forms and algebraic structure
Author: Greitz, Jesper
Awarding Body: King's College London (University of London)
Current Institution: King's College London (University of London)
Date of Award: 2012
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The following thesis will be concerned with various aspects of supergravity theories in a superspace setting, focusing mainly on maximal and half-maximal theories in three dimensions and maximal theories in ten-dimensions. For the three-dimensional theories it is convenient to start from an off-shell superconformal geometry valid for any number of supersymmetries. We first apply this formalism to show that it is consistent to couple ABJM and BLG theory to conformal supergravity, in doing so we find that N = 8 superconformal matter can also be charged under the gauge group SO(N). By imposing further constraints on the off-shell superconformal geometry, we obtain half-maximal and maximal Poincare supergravity. We solve for the geometry at dimension one in the half-maximal case with sigma models of the form (SO(8) x SO(n))\SO(8, n), and for the complete geometry in the maximal theory, where the scalar fields live in the coset SO(16)\E8. Using the Ricci identity, we also derive the equations of motion for the scalar and fermion fields in the latter theory. Using supersymmetry and duality we derive the form spectrum of the above Poincare supergravity theories and of type IIA and IIB supergravity in ten dimensions. Particular we show that the consistent Bianchi identities, which are not guaranteed to be satisfied from cohomology, determine a Lie super co-algebra. We derive the Cartan matrices of the dual algebras which are Borcherds algebras. The Cartan matrices can be used to generate the entire form field spectrum. We study gaugings of half-maximal and maximal Poincare supergravity in three dimensions by introducing a non-abelian gauged subgroup of the duality group and making use of the gauged Maurer-Cartan form. The differential forms can also be studied in the gauged theory by deforming the Bianchi identities. The closure of the full system of forms requires the presence of D + 2-form field strengths in the supergravity limit. In superspace, the Borcherds algebras predict an infinite number of form fields of degree larger than that of space-time. Indeed all those of degree larger than D + 2 are zero in supergravity, although this might change in string theory. We provide some evidence that a six-form, in half-maximal supergravity in three dimensions can become non-zero in the presence of α'-corrections.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available