AbstractThe overarching theme of this thesis is the study of ﬁeld theories generically without Lorentz symmetry, but possessing an inhomogeneous scaling symmetry. A number of aspects of such models are explored, including the addition of supersymmetry, as well as their application in the construction of more conventional conformal ﬁeld theories.
In Part I, we describe a scaling technique by which non-Lorentzian theories with an inhomogeneous scaling symmetry are obtained from Lorentzian supersymmetric models, while crucially retaining all supersymmetry of the parent theory. The dynamics of the resulting theories are generically constrained to the moduli space of some BPS soliton. We explore this scaling technique and the resulting reduction to moduli space superconformal quantum mechanics for some examples, including several relevant to the branes of M-theory.
In Part II, we build from the ground up the theory of models in ﬁve dimensions with an exotic SU(1, 3) spacetime symmetry, which includes an inhomogeneous scaling. After deriving and solving the corresponding Ward-Takahashi identities for correlators, we demonstrate how such models naturally describe any six-dimensional conformal ﬁeld theory on a conformal compactiﬁcation of Minkowski space. In doing so, we derive necessary conditions for a generic SU(1, 3) theory to admit such a six-dimensional interpretation, and also ex-plore a degenerate limit of the construction that recovers the standard Discrete Lightcone Quantisation picture. Finally, we study in detail an explicit SU(1, 3) model found through the technique of Part I, which is conjectured to provide a Lagrangian description of the non-Abelian (2, 0) theory. The theory is shown to realise six-dimensional physics through the inclusion of singular points carrying non-zero instanton charge, which are encoded by instanton operators in the path integral. We further explore the constrained dynamics of the theory, which are shown to describe the propagation of Yang-Mills instanton-particles between such points.
|Date of Award
|1 Oct 2021
|Neil Lambert (Supervisor)