Constrained gauge fields from spontaneous Lorentz violation

We reconsider the possibility of violating the generalized second law of thermodynamics in theories with spontaneous Lorentz violation. It has been proposed that this may be accomplished in particular with a black hole immersed in a ghost condensate background, which may be taken to break Lorentz invariance without appreciably distorting the space-time geometry. In this paper we show that there in fact exist solutions explicitly describing the flow of negative energy into these black holes, allowing for violation of the second law in a very simple way. This second law violation is independent of any additional assumptions such as couplings of the ghost condensate to secondary fields, and suggests that violation of the null energy condition may be the true source of pathology in these theories.

We compare the Lorentz violation terms of the pure photon sector between two field theory models, namely, the minimal standard model extension (SME) and the standard model supplement (SMS). From the requirement of the identity of the intersection for the two models, we find that the free photon sector of the SMS can be a subset of the photon sector of the minimal SME. We not only obtain some relations between the SME parameters but also get some constraints on the SMS parameters from the SME parameters. The CPT-odd coefficients(kAF)αof the SME are predicted to be zero. There are 15 degrees of freedom in the Lorentz violation matrixΔαβof free photons of the SMS related with the same number of degrees of freedom in the tensor coefficients(kF)αβμν, which are independent from each other in the minimal SME but are interrelated in the intersection of the SMS and the minimal SME. With the related degrees of freedom, we obtain the conservative constraints(2σ)on the elements of the photon Lorentz violation matrix. The detailed structure of the photon Lorentz violation matrix suggests some applications to the Lorentz violation experiments for photons.

This work deals with the dynamics of inflation in the context of a\nscalar-vector-tensor theory of gravity exhibiting spontaneous Lorentz violation\nat early times. We describe a first-order formalism which we use to obtain new\nexact Lorentz violating inflationary solutions for a broad family of models,\nsome in the absence of a potential for the inflaton field. Our results show\nthat different conditions are required to solve the horizon and flatness\nproblems. In particular, we find a necessary condition for inflation to provide\na solution to both problems and we show that in inflationary models with no\ninflaton potential a period of superinflation might be necessary to solve the\nflatness problem.\n

Frohlich, Morchio and Strocchi long ago proved that the Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where the consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected “Sky” group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These Abelian considerations and model are extended to non-Abelian gauge symmetries. Basic issues regarding the observability of twisted non-Abelian gauge symmetries and of the asymptotic ADM symmetries of quantum gravity are raised.

We study CPT and Lorentz violation in the electroweak gauge sector of the Standard Model in the context of the Standard-Model Extension (SME). In particular, we show that any non-zero value of a certain relevant Lorentz violation parameter that is thus far unbounded by experiment would imply that for sufficiently large energies one of the helicity modes of the Z boson should propagate with spacelike four-momentum and become stable against decay in vacuum. In this scenario, Cherenkov-like radiation of Z bosons by ultra-high-energy cosmic-ray protons becomes possible. We deduce a bound on the Lorentz violation parameter from the observational data on ultra-high energy cosmic rays.

The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate $n$-point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.

In the context of conventional quantum field theory, we present a general Lorentz-violating extension of the minimal $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ standard model including $\mathrm{CPT}$-even and $\mathrm{CPT}$-odd terms. It can be viewed as the low-energy limit of a physically relevant fundamental theory with Lorentz-covariant dynamics in which spontaneous Lorentz violation occurs. The extension has gauge invariance, energy-momentum conservation, and covariance under observer rotations and boosts, while covariance under particle rotations and boosts is broken. The quantized theory is Hermitian and power-counting renormalizable, and other desirable features such as microcausality, positivity of the energy, and the usual anomaly cancellation are expected. Spontaneous symmetry breaking to the electromagnetic U(1) is maintained, although the Higgs expectation is shifted by a small amount relative to its usual value and the ${Z}^{0}$ field acquires a small expectation. A general Lorentz-breaking extension of quantum electrodynamics is extracted from the theory, and some experimental tests are considered. In particular, we study modifications to photon behavior. One possible effect is vacuum birefringence, which could be bounded from cosmological observations by experiments using existing techniques. Radiative corrections to the photon propagator are examined. They are compatible with spontaneous Lorentz and $\mathrm{CPT}$ violation in the fermion sector at levels suggested by Planck-scale physics and accessible to other terrestrial laboratory experiments.

Chiral composite fermions without U(1)'s

Enlarged Peccei-Quinn symmetry and limits from the supernova

We discuss a number of experimental constraints on Weinberg's Higgs portal model. In this framework, the standard model (SM) particle spectrum is extended to include one complex scalar field $S$ and one Dirac fermion $\ensuremath{\psi}$. These new fields are singlets under the SM gauge group and are charged under a global $U(1)$ symmetry. Breaking of this $U(1)$ symmetry results in a massless Goldstone boson $\ensuremath{\alpha}$ and a massive $CP$-even scalar $r$ and splits the Dirac fermion into two new mass-eigenstates ${\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}$, corresponding to Majorana fermions. The interest on such a minimal SM extension is twofold. On the one hand, if the Goldstone bosons are in thermal equilibrium with SM particles until the era of muon annihilation, their contribution to the effective number of neutrino species can explain the hints from cosmological observations of extra relativistic degrees of freedom at the epoch of last scattering. On the other hand, the lightest Majorana fermion ${\ensuremath{\psi}}_{\ensuremath{-}}$ provides a plausible dark matter candidate. Mixing of $r$ with the Higgs doublet $\ensuremath{\phi}$ is characterized by the mass of hidden scalar ${m}_{h}$ and the mixing angle $\ensuremath{\theta}$. We constrain this parameter space using a variety of experimental data, including heavy meson decays with missing energy, the invisible Higgs width, and direct dark matter searches. We show that different experimental results compress the allowed parameter space in complementary ways, covering a large range of ${\ensuremath{\psi}}_{\ensuremath{-}}$ masses ($5\ensuremath{\lesssim}{m}_{\ensuremath{-}}\ensuremath{\lesssim}100\text{ }\text{ }\mathrm{GeV}$). Though current results narrow the parameter space significantly (for the mass range of interest, $\ensuremath{\theta}\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$ to ${10}^{\ensuremath{-}4}$), there is still room for discovery ($\ensuremath{\alpha}$ decoupling at the muon annihilation era requires $\ensuremath{\theta}\ensuremath{\gtrsim}{10}^{\ensuremath{-}5}$ to ${10}^{\ensuremath{-}4}$). In the near future, measurements from ATLAS, CMS, LHCb, NA62, XENON1T, LUX, and CDMSlite will probe nearly the full parameter space.

Even though models with spontaneous Lorentz-symmetry breaking also damage gauge invariance, an interesting possibility that emerges is to interpret the resultant massless Goldstone bosons as the gauge bosons of the related gauge theory. In this contribution we review the conditions under which gauge invariance is recovered from such models. To illustrate our general approach we consider the classical Abelian bumblebee and Nambu models. In the former case we prove its connection with electrodynamics by a procedure which takes proper care of the gauge-fixing conditions. In the case of the Abelian Nambu model its relation with electrodynamics is established in such a way that the generalization to the non-Abelian case is straightforward.

We consider neutrino oscillations in the minimal Standard-Model Extension describing general Lorentz and CPT violation. Among the models without neutrino mass differences is one with two degrees of freedom that reproduces most major observed features of neutrino behavior.

Interactions of gauge-invariant systems are severely constrained by several consistency requirements. One is the preservation of the number of gauge symmetries, another is causal propagation. For lower-spin fields, the emphasis is usually put on gauge invariance that happens to be very selective by itself. We demonstrate with an explicit example, however, that gauge invariance, albeit indispensable for constructing interactions, may not suffice as a consistency condition. The chosen example that exhibits this feature is the theory of a massless spin-$3/2$ field coupled to electromagnetism. We show that this system admits an electromagnetic background in which the spin-$3/2$ gauge field may move faster than light. Requiring causal propagation rules out otherwise allowed gauge-invariant couplings. This emphasizes the importance of causality analysis as an independent test for a system of interacting gauge fields. We comment on the implications of allowing new degrees of freedom and nonlocality in a theory, on higher-derivative gravity and Vasiliev's higher-spin theories.

Duality equivalence between self-dual and topologically massive non-abelian models

The Scotogenic model is an economical scenario that generates neutrino masses at the 1-loop level and includes a dark matter candidate. This is achieved by means of an ad-hocZ2 symmetry, which forbids the tree-level generation of neutrino masses and stabilizes the lightest Z2-odd state. Neutrino masses are also suppressed by a quartic coupling, usually denoted by λ5. While the smallness of this parameter is natural, it is not explained in the context of the Scotogenic model. We construct an ultraviolet completion of the Scotogenic model that provides a natural explanation for the smallness of the λ5 parameter and induces the Z2 parity as the low-energy remnant of a global U(1) symmetry at high energies. The low-energy spectrum contains, besides the usual Scotogenic states, a massive scalar and a massless Goldstone boson, hence leading to novel phenomenological predictions in flavor observables, dark matter physics and colliders.