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Register a new userNew Setting for Spontaneous Gauge Symmetry Breaking?
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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.
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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.
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 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.
In this paper we discuss a disordered $d$-dimensional Euclidean $lambdavarphi^{4}$ model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each replica partition function, using the saddle-point equations and imposing the replica symmetric ansatz, we show the presence of a spontaneous symmetry breaking mechanism in the disordered model. Moreover, the leading replica partition function must be described by a large-$N$ Euclidean replica field theory. We discuss finite temperature effects considering periodic boundary condition in Euclidean time and also using the Landau-Ginzburg approach. In the low temperature regime we prove the existence of $N$ instantons in the model.
We consider some aspects of spontaneous breaking of Lorentz Invariance in field theories, discussing the possibility that the certain tensor operators may condensate in the ground state in which case the tensor Goldstone particles would appear. We analyze their dynamics and discuss to which extent such a theory could imitate the gravity. We are also interested if the universality of coupling of such `gravitons with other particles can be achieved in the infrared limit. Then we address the more complicated models when such tensor Goldstones coexist with the usual geometrical gravitons. At the end we examine the properties of possible cosmological scenarios in the case of goldstone gravity coexisting with geometrical gravity.
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