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Title: A new gauge/gravity dictionary via the division algebras
Author: Nagy, Silvia
ISNI:       0000 0004 7233 0041
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2015
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The main goal of this thesis is to explore the idea of gravity as the square of a gauge theory at the level of Lagrangian symmetries. By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the at space Yang-Mills symmetries of local gauge invariance and global super-Poincare. As an example, we will we focus on the new-minimal (12 + 12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4 + 4;N_L = 1) and (3 + 0;N_R = 0). By tensoring all possible pairs of on-shell super Yang-Mills multiplets in dimensions 3 ≤ D ≤ 10 to get on-shell supergravity multiplets, possibly with additional matter multiplets. By associating a (direct sum of) division algebra(s) D with each dimension 3 ≤ D ≤ 10 we obtain a formula for the supergravity U-duality G and its maximal compact subgroup H in terms of the internal global symmetry algebras of each super Yang-Mills theory. We then extend our analysis to include supergravities coupled to an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor product. We also introduce the idea of writing the SYM multiplets themselves as a double copy. We construct the states and symmetries of N = 4 super-Yang-Mills by tensoring two N = 1 chiral multiplets and introducing two extra SUSY generators. This allows us to write the maximal N = 8 supergravity as four copies of the chiral multiplet. We extend this to higher dimensions and discuss possible applications.
Supervisor: Duff, Michael Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral