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Unifying Conformal Gravity and the Standard Model of particle physics

Dirksen, K. (2017) Unifying Conformal Gravity and the Standard Model of particle physics. Master's Thesis / Essay, Physics.

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This thesis is a literature study centered around the question `How can we use conformal invariance to unify the Standard Model with Gravity?' After refreshing the Standard Model and renormalization and regularization techniques, as well as Einstein's theory of General Relativity, it is explained why conformal invariance is a useful tool in the unification program. The differences between the related concepts of `conformal', `scale' and `Weyl' invariance are explained and the two types of Conformal Gravity theories are introduced: Conformal Weyl gravity based on the squared Weyl tensor and Conformal Dilaton Gravity which uses a Stückelberg trick to turn the Einstein-Hilbert action into a conformally invariant theory. Pursuing the latter due to unitarity concerns in the former, the Conformal Standard Model in the presence of gravity is developed. We distinguish between two toy models, one with an unphysical scalar dilaton field and one with a physical dilaton. As conformal invariant theories do not allow the explicit presence of scales, conformal symmetry breaking is necessary to generate the scale needed for electroweak symmetry breaking (EWSB). The Weyl invariance of the theory with the unphysical dilaton can be extended to the quantum theory and the additional gauge freedom allows gauge fixing of the dilaton to a constant, thus ensuring EWSB. The theory with the physical dilaton suffers from a conformal anomaly. Boldly assuming that this anomaly is cancelled at some scale, a Gildener-Weinberg analysis of the theory shows the possibility of radiative breaking of the conformal symmetry. The two theories differ in one minus sign, but have vastly different results. Experiments and astronomical observations could help in understanding which, if any, of these theories could be a toy model for a Theory of Everything.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Physics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 08:27
Last Modified: 15 Feb 2018 08:27

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