A geodesic model in conformal superspace
Year: 2016
Type: preprint
Abstract: Following [1], I look for the most general geometrodynamical symmetries compatible with spatial relational principles. I argue that they lead either to a completely static Universe, or one embodying spatial conformal dieomorphisms. Demanding locality for an action compatible with these principles severely limits its form, both for the gravitational part as well as all matter couplings. The simplest and most natural choice for pure gravity has two propagating physical degrees of freedom (and no refoliation-invariance). The system has a geometric interpretation as a geodesic model in innite dimensional conformal superspace. Conformal superspace is a stratied manifold, with dierent strata corresponding to dierent isometry groups. Choosing space to be (homeomorphic to) S 3 , conformal superspace has a preferred stratum with maximal stabilizer group. This stratum consists of a single point { corresponding to the conformal geometry of the round 3-sphere. This is the most homogeneous non-degenerate geometry. The path integral transition amplitude from this special initial condition denes a unique, static, wave-functional over conformal superspace. This and the lack of refoliation invariance allow me to implement an unusual sort of gauge-xing: given the initial representative of the gauge orbit, it xes the path velocities to be parallel propagated, i.e. it xes a horizontal lift for each path in the principal ber bundle as opposed to a section of the principal ber bundle, as is usually done. This facilitates the writing of the Fadeev-Popov determinant for our system and its BRST symmetries, and completely determines the gauge-xed path integral, which can be shown to be Weyl-anomaly free.
Source: arXiv (Cornell University)
Author: Henrique Gomes
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2294067521