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, 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.
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Wetterich, C. Pregeometry and spontaneous time-space asymmetry. J. High Energ. Phys. 2022, 69 (2022). https://doi.org/10.1007/JHEP06(2022)069
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DOI: https://doi.org/10.1007/JHEP06(2022)069