  We consider a model with gauged baryon number that may be rendered
asymptotically safe when gravitational effects above the Planck scale are taken
into account. We study the ultraviolet fixed points in this theory and
determine the restrictions on the parameter space of the model at the TeV scale
following from the requirement that the asymptotic fixed points are reached.
Assuming that the new gauge symmetry is broken at the TeV scale, we comment on
the phenomenological implications of these restrictions.
