38 research outputs found
Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance
Recently, it has been pointed out that dimensionless actions in four
dimensional curved spacetime possess a symmetry which goes beyond scale
invariance but is smaller than full Weyl invariance. This symmetry was dubbed
{\it restricted Weyl invariance}. We show that starting with a restricted Weyl
invariant action that includes a Higgs sector with no explicit mass, one can
generate the Einstein-Hilbert action with cosmological constant and a Higgs
mass. The model also contains an extra massless scalar field which couples to
the Higgs field (and gravity). If the coupling of this extra scalar field to
the Higgs field is negligibly small, this fixes the coefficient of the
nonminimal coupling between the Higgs field and gravity. Besides the
Higgs sector, all the other fields of the standard model can be incorporated
into the original restricted Weyl invariant action.Comment: 7 pages, no figure
Enlarging the symmetry of pure gravity, BRST invariance and its spontaneous breaking
Pure gravity was considered originally to possess only global scale
symmetry. It was later shown to have the larger restricted Weyl symmetry where
it is invariant under the Weyl transformation when the conformal factor obeys the harmonic condition
. Restricted Weyl symmetry has an analog in gauge theory.
Under a gauge transformation , the gauge-fixing term has a residual gauge
symmetry when . In this paper, we consider scenarios where the
symmetry of pure gravity can be enlarged even further. In one scenario,
we add a massless scalar field to the pure gravity action and show that
the action becomes on-shell Weyl invariant when the equations of motion are
obeyed. We then enlarge the symmetry to a BRST symmetry where no on-shell or
restricted Weyl condition is required. The BRST transformations here are not
associated with gauge transformations (such as diffeomorphisms) but with Weyl
(local scale) transformations where the conformal factor consists of a product
of Grassmann variables. BRST invariance in this context is a generalization of
Weyl invariance that is valid in the presence of the Weyl-breaking term.
In contrast to the BRST invariance of gauge theories like QCD, it is not
preserved after quantization since renormalization introduces a scale (leading
to the well-known Weyl (conformal) anomaly). We show that the spontaneous
breaking of the BRST symmetry yields an Einstein action; this still has a
symmetry which is also anomalous. This is in accord with previous work that
shows that there is conformal anomaly matching between the unbroken and broken
phases when conformal symmetry is spontaneously broken.Comment: 13 pages, no figure