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Title: Supergravity as Yang-Mills Squared
Author: Zoccali, Michele
ISNI:       0000 0004 7658 9069
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2019
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This thesis is concerned with the study of various aspects of the Yang-Mills Squared construction, which aims at furthering our understanding of the provocative idea that gravity may be regarded, in some sense, as the "square" of gauge theory. By assuming a convolutive tensor product and introducing a bi-adjoint scalar fi eld as one of the factors, the Yang-Mills Squared formalism describes a purely field-theoretic realisation of this correspondence: the content as well as the global U-duality symmetries of a wide variety of supergravity theories may be shown to originate in the product of the contents and R-symmetries of two super Yang-Mills theories. Here we apply these ideas to twin supergravities, pairs of theories with identical bosonic sectors but di fferent supersymmetric completions, to demonstrate that they are related in a controlled fashion through the underlying Yang-Mills factors. This has the additional advantage of giving a prescription for constructing new examples of factorisable supergravities from known ones. The second part of the thesis is devoted to the study of the gauge symmetries of linearised axion-dilaton gravity by adopting a Becchi-Rouet-Stora-Tyutin (BRST) covariant formulation of Yang-Mills. The content, BRST and anti-BRST transformations as well as the equations of motion of the gravitational side are shown to be related to those of the gauge theory side by means of a dictionary building the gravity fields as sums of convolutions of Yang-Mills potentials and ghosts, thus providing a fully Lorentz-covariant version of the Yang-Mills Squared map. The anti-BRST transformations of the Kalb-Ramond 2-form sector are shown to naturally anti-commute with BRST in this formalism.
Supervisor: Duff, Michael Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral