Year: 2016
Type: article
Abstract: According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected $SO(n)$ connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an $SO(n\ensuremath{-}1,1)$ connection on the spacetime. The principal fiber bundle character of the original $SO(n)$ guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Authors: Benjamin C. Lovelady, James T. Wheeler
Institution: Utah State University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2194420505