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Thesis
Symmetry breaking in projective gauge gravity
University of Iowa
Master of Science (MS), University of Iowa
Spring 2024
DOI: 10.25820/etd.007318
Abstract
The Thomas-Whitehead (TW) projective theory of gravity has its origin in 1 + 1(+1) dimensional string theory. The coadjoint elements of the Virasoro algebra contain the Diffeomorphism field, identified by its transformation behavior under the coadjoint action. Through a correspondence with Sturm-Liouville operators, the Diffeomorphism field is identified with the potential. When lifted to a higher dimensional classical theory, the Diffeomorphism field appears as a component of a projective connection.
In m spacetime dimensions, the projective spin connection, rather, the framed projective connection appears as a nonlinear connection taking values in the Lie algebra of a particular subgroup of the general linear group in m + 1 dimensions. These vertical translations are restored and a composite coset element is formed. The resulting nonlinear connection may be viewed as a general pre-projective connection. Emphasis is put on the utilization of covariant generalized Higgs fields in this construction. Some properties of the present connection are investigated and compared with what is known about the TW projective connection.
This document seeks a basis-independent description of projective gravity, wherein the recently discovered Diffeomorphism field retains dynamics. Without an additional metric structure, only one option presents itself as a governing action functional. The projective Pontryagin density is formed and the associated Chern-Simons forms computed. The latter appear nearly identical to the Chern-Simons forms of Metric-Affine gravitational gauge theories coupled to a scalar field when expanded about the maximally symmetric (anti) de Sitter solutions. In a similar fashion, the associated field equations serve to produce the Bianchi identities.
Once a metric structure is introduced, further action functionals become available. However, this imposition requires the stability group be Lorentzian. This makes available a notion of Lie algebra dual. Two dual operations are considered. The first follows the work of Stelle and West, utilizing a fundamental algebraic vector field to explicitly reduce the symmetry group. The second is an ordinary duality, which is utilized to form a Lovelock-type action. Both models are solved and discussed. None of these models appear to produce dynamics for the Diffeomorphism field.
Matter fields are here considered in the nonlinear setting. This straight-forward process reveals a discrepancy when compared to the common uses of projective matter fields. In avoidance of this, the common form is adopted and all new structure reduced, such that the setting which results is that of TW theory. The TW-Dirac model is revisited and written in a manifestly covariant form upon the dimensional reduction to spacetime. A non-hermitian chiral coupling to the Diffeomorphism scalar is re-confirmed. However, the induced chiral mass is shown to contain both hermiticity-respecting and violating contributions. The implications of this are left for future work.
Details
- Title: Subtitle
- Symmetry breaking in projective gauge gravity
- Creators
- Michael J. Connolly
- Contributors
- Vincent G.J. Rodgers (Advisor)Kory Stiffler (Committee Member)Wayne Polyzou (Committee Member)Palle Jorgensen (Committee Member)
- Resource Type
- Thesis
- Degree Awarded
- Master of Science (MS), University of Iowa
- Degree in
- Physics
- Date degree season
- Spring 2024
- Publisher
- University of Iowa
- DOI
- 10.25820/etd.007318
- Number of pages
- viii, 97 pages
- Copyright
- Copyright 2024 Michael J. Connolly
- Language
- English
- Date submitted
- 04/23/2024
- Description bibliographic
- Includes bibliographical references (pages 91-97).
- Public Abstract (ETD)
- Symmetry is a foundational aspect of nature, as is obvious when looking outside. These symmetries can be described elegantly in the language of nature: Mathematics. Since change is the only true constant in nature, a natural question arises: What were the symmetries of nature before this moment in spacetime? The many humans who have contributed in answering this question point towards particular organizational principles. Essentially, aspects of nature must reorganize over time in order to maintain existence. For example, hot and energetic steam full of random and chaotic motion must reorganize itself into a reasonably behaved pattern when cooled below freezing. This emergence of visual symmetry (pattern) is actually the result of losing symmetry. Applying these organizational principles to objects (matter) existing within some environment (the universe / spacetime) leads one to the Standard Model of Particle Physics. This document seeks to address whether the environment itself is subject to principles of organization. Projective geometry is the geometry of perspective and it is well known Humans perceive their environment projectively. This idea may serve as a bridge to understanding the organizational principles of environment itself, since it is likely this description of perspective is not unique to Humans. Rather, this may be a property of interaction and information exchange, something that necessitates environment. By attributing projective properties to the environment (spacetime), and investigating the corresponding symmetry, there appears a new physical object (particle / field). This object has the potential to address and explain many open questions regarding the nature of existence.
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984647645602771
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