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Register a new userWeyl gauge symmetry and its spontaneous breaking in Standard Model and inflation
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We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the Standard Model (SM) and inflation. In models with non-minimal couplings of the scalar fields to the Ricci scalar, that are conformal invariant, the spontaneous generation by a scalar field(s) vev of a positive Newton constant demands a negative kinetic term for the scalar field, or vice-versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field $omega_mu$ couples to the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The field $omega_mu$ undergoes a Stueckelberg mechanism and becomes massive after eating the (radial mode) would-be-Goldstone field (dilaton $rho$) in the scalar sector. Before the decoupling of $omega_mu$, the dilaton can act as UV regulator and maintain the Weyl symmetry at the {it quantum} level, with relevance for solving the hierarchy problem. After the decoupling of $omega_mu$, the scalar potential depends only on the remaining (angular variables) scalar fields, that can be the Higgs field, inflaton, etc. We show that successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with $omega_mu$ introduced to avoid ghosts, the natural framework is that of Weyl geometry which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative.
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Over half century ago Carl Brans participated in the construction of a viable deformation of the Einstein gravity theory. Their suggestion involves expanding the tensor-based theory by a scalar field. But experimental support has not materialized. Nevertheless the model continues to generate interest and new research. The reasons for the current activity is described in this essay, which is dedicated to Carl Brans on his eightieth birthday.
Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of inertial spontaneous symmetry breaking that does not involve a potential. This is dictated by the structure of the Weyl current, $K_mu$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEVs of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.
We propose a new construction of the supergravity inflation as an UV completion of the Higgs-$R^2$ inflation. In the dual description of $R^2$-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singlet scalar fields. We also discuss supersymmetry breaking and its transmission to the visible sector as a result of the couplings of the dual chiral superfields and the non-minimal gravity coupling of the Higgs fields.
We study baryogenesis in effective field theories where a $mathrm{U}(1)_{ B-L}$-charged scalar couples to gravity via curvature invariants. We analyze the general possibilities in such models, noting the relationships between some of them and existing models, such as Affleck-Dine baryogenesis. We then identify a novel mechanism in which $mathrm{U}(1)_{ B-L}$ can be broken by couplings to the Gauss-Bonnet invariant during inflation and reheating. Using analytic methods, we demonstrate that this mechanism provides a new way to dynamically generate the net matter-anti-matter asymmetry observed today, and verify this numerically.
We argue that there is a spontaneously broken rotational symmetry between space-time coordinates and gauge theoretical phases. The dilatonic mode acts as the massive Higgs boson, whose vacuum expectation value determines the gauge couplings. This mechanism requires that the quadratic divergences, or tadpoles of the three gauge-theory couplings, unify at a certain scale. We verify this statement, and find that this occurs at Lambda_u ~ 4x10^7 GeV. The tadpole cancellation condition, together with the dilaton self-energy, fixes the value of the unified tadpole coefficient to be 1/[4 ln(Lambda_cut/Lambda_u)]. The observed values of the coupling constants at Lambda_u then implies Lambda_cut ~ 4x10^18 GeV, which is close to the value of the reduced Planck mass MR_Pl=M_Pl/sqrt(8 pi)=2.4 x 10^18 GeV. In other words, by assuming a cutoff at M_Pl or MR_Pl, we are able to obtain predictions for the gauge couplings which agree with the true values to within a few percent. It turns out that this symmetry breaking can only take place if mass is generated with the aid of some other means such as electroweak symmetry breaking. Assuming dynamical symmetry breaking originating at MR_Pl, we obtain M_chi ~ 10^9 GeV, which is not unreasonable but somewhat higher than Lambda_u. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three.
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