Physics Student Research

Document Type

Article

Journal/Book Title/Conference

Physical Review D

Volume

93

Issue

8

Publication Date

4-15-2016

First Page

085002-1

Last Page

085002-11

DOI

http://dx.doi.org/10.1103/PhysRevD.93.085002

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−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.

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