Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stueckelberg breaking of Weyl conformal geometry with applications to
  gravity   Weyl conformal geometry may play a role in early cosmology where effective
theory at short distances becomes conformal. Weyl conformal geometry also has a
built-in geometric Stueckelberg mechanism: it is broken spontaneously to
Riemannian geometry after a Weyl gauge transformation (of "gauge fixing") while
Stueckelberg mechanism re-arranges the degrees of freedom, conserving their
number ($n_{df}$). The Weyl gauge field ($\omega_\mu$) of local scale
transformations acquires a mass after absorbing a compensator (dilaton),
decouples, and Weyl connection becomes Riemannian. Mass generation has thus a
dynamic origin, as a transition from Weyl to Riemannian geometry. We show that
a "gauge fixing" symmetry transformation of the original Weyl quadratic gravity
action in its Weyl geometry formulation immediately gives the Einstein-Proca
action for the Weyl gauge field and a positive cosmological constant, plus
matter action (if present). As a result, the Planck scale is an {\it emergent}
scale, where Weyl gauge symmetry is spontaneously broken and Einstein action is
the broken phase of Weyl action. This is in contrast to local scale invariant
models (no gauging) where a negative kinetic term (ghost dilaton) remains
present and $n_{df}$ is not conserved when this symmetry is broken. The mass of
$\omega_\mu$, setting the non-metricity scale, can be much smaller than
$M_\text{Planck}$, for ultraweak values of the coupling ($q$). If matter is
present, a positive contribution to the Planck scale from a scalar field
($\phi_1$) vev induces a negative (mass)$^2$ term for $\phi_1$ and spontaneous
breaking of the symmetry under which it is charged. These results are immediate
when using a Weyl geometry formulation of an action instead of its Riemannian
picture. Briefly, Weyl gauge symmetry is physically relevant and its role in
high scale physics should be reconsidered.

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin