Dynamical spacetime symmetry

TL;DR

This paper explores a novel approach to gauge gravity, showing how a specific gauging of conformal symmetry can produce a spacetime with Lorentzian signature and internal symmetries, aligning with quantum field theory constraints.

Contribution

It demonstrates that biconformal gauging of conformal symmetry can lead to a spacetime with Lorentzian signature and internal symmetries, providing an alternative to traditional gauge theories of gravity.

Findings

Biconformal gauging doubles Euclidean space dimension to form a symplectic manifold.

The solder form becomes Lorentzian in the flat case.

Coordinate invariance induces an SO(n-1,1) connection on spacetime.

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-dim 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.