Pregeometry and spontaneous time-space asymmetry

TL;DR

This paper explores how the distinction between time and space could emerge dynamically from a pregeometric Yang-Mills model with fermions, where geometry and relativity arise from spontaneous symmetry breaking.

Contribution

It introduces a Yang-Mills framework with non-compact gauge group to derive spacetime signature and geometry from spontaneous symmetry breaking, rather than assuming them a priori.

Findings

Spontaneous symmetry breaking induces time-space asymmetry.

Emergence of geometry and general relativity at large distances.

Model potentially consistent with unitarity and well-behaved at short distances.

Abstract

In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of a model. For short distances we formulate our model as a Yang-Mills theory with fermions and vector fields. For the local gauge symmetry we take the non-compact group SO(4,\,$\mathbb{C}$). The particular representation of the vector field permits us to implement diffeomorphism invariant kinetic terms. Geometry and general relativity emerge at large distances due to a spontaneous breaking of the gauge symmetry which induces masses for the gauge bosons. The difference between time and space arises directly from this spontaneous symmetry breaking. For a euclidean metric all fields have a standard propagator at high momenta. Analytic continuation to a Minkowski-metric is achieved by a change of field values. We conjecture that this type of model could be consistent with unitarity and well behaved in the short distance limit.