Pregeometry and spontaneous time-space asymmetry

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, 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.

Automated summary

This paper investigates the emergence of metrics in pregeometry and proposes a model where the distinction between time and space arises from the dynamics. By formulating the model as a Yang-Mills theory with fermions and vector fields, geometry and general relativity emerge at large distances due to spontaneous symmetry breaking. The paper suggests that this type of model may behave consistently and well in the short distance limit.