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We introduce new Lorentz-symmetry violating kinematics for a four-fermion interaction model, where dynamical mass generation is allowed, irrespective of the strength of the coupling. In addition, these kinematics lead to a quasirelativistic dispersion relation, in the sense that it is relativistic in both the infrared and the ultraviolet, but not in an intermediate regime, characterized by the mass M. For two fermions, we show that a flavor-mixing mass matrix is generated dynamically, and the Lorentz symmetric limit M?8 leads to two free relativistic fermions, with flavor oscillations. This model, valid for either Dirac or Majorana fermions, can describe any set of phenomenological values for the eigenmasses and the mixing angle. [ABSTRACT FROM AUTHOR]

In the context of dynamical breaking of local supersymmetry (supergravity), including the Deser-Zumino super-Higgs effect, for the simple but quite representative cases of N = 1, D = 4 supergravity, we discuss the emergence of Starobinsky-type inflation, due to quantum corrections in the effective action arising from integrating out gravitino fields in their massive phase. This type of inflation may occur after a first-stage small-field inflation that characterizes models near the origin of the one-loop effective potential, and it may occur at the nontrivial minima of the latter. Phenomenologically realistic scenarios, compatible with the Planck data, may be expected for the conformai supergravity variants of the basic model. [ABSTRACT FROM AUTHOR]

We investigate the dynamical breaking of local supersymmetry (supergravity), including the Deser- Zumino super-Higgs effect, via the corresponding one-loop effective potential for the simple but quite representative cases of N = 1, D = 4 simple supergravity and a (simplified) conformai version of it. We find solutions to the effective equations which indicate dynamical generation of a gravitino mass, thus breaking supergravity. In the case of conformai supergravity models, the gravitino mass can be much lower than the Planck scale, for global supersymmetry breaking scales below the grand unification scale. The absence of instabilities in the effective potential arising from the quantum fluctuations of the metric field is emphasized, contrary to previous claims in the literature. [ABSTRACT FROM AUTHOR]

We study consequences of Lorentz symmetry violation in az=2 Lifshitz extension of QED in 3 + 1 dimensions, and we discuss nontrivial effects of quantization. Because of the specific power of space momentum in propagators of the model, dimensional regularization leads to an unusual interpretation of loop integrals, which are finite even when the space dimension goes to the integer 3. We check the consistency of the approach by calculating the (vanishing) corrections to the photon mass and the IR-divergence-free corrections to the dispersion relation for massless fermions. [ABSTRACT FROM AUTHOR]

We show how a mass mixing matrix can be generated dynamically, for two massless fermion flavors coupled to a Lorentz invariance violating (LIV) gauge field. The LIV features play the role of a regulator for the gap equations, and the nonanalytic dependence of the dynamical masses, as functions of the gauge coupling, allows us to consider the limit where the LIV gauge field eventually decouples from the fermions. Lorentz invariance is then recovered, to describe the oscillation between two free fermion flavors, and we check that the finite dynamical masses are the only effects of the original LIV theory. We also discuss briefly a connection of our results with the case of Majorana neutrinos in both, the standard model, where only left-handed (active) neutrinos are considered, and extensions thereof, with sterile righthanded neutrinos. [ABSTRACT FROM AUTHOR]

We consider a four-dimensional field-theory model with two massless fermions, coupled to an Abelian vector field without flavor mixing, and to another Abelian vector field with flavor mixing. Both Abelian vectors have a Lorentz-violating kinetic term, introducing a Lorentz-violation mass scale M, from which fermions and the flavor-mixing vector get their dynamical masses, whereas the vector coupled without flavor mixing remains massless. When the two coupling constants have similar values in order of magnitude, a mass hierarchy pattern emerges, in which one fermion is very light compared to the other, while the vector mass is of the order of the heavy fermion mass. The work presented here may be considered as a Lorentz-symmetry-violating alternative to the Higgs mechanism, in the sense that no scalar particle (fundamental or composite) is necessary for the generation of the vector-meson mass. However, the model is not realistic given that, as a result of Lorentz violation, the maximal (light-cone) speed seen by the fermions is smaller than that of the massless gauge boson (which equals the speed of light in vacuo) by an amount which is unacceptably large to be compatible with the current tests of Lorentz invariance, unless the gauge couplings assume unnaturally small values. Possible ways out of this phenomenelogical drawback are briefly discussed, postponing a detailed construction of more realistic models for future work. [ABSTRACT FROM AUTHOR]

In this note we examine whether spherically symmetric solutions in covariant Horava-Lifshitz gravity can reproduce Newton's Law in the IR limit λ → 1. We adopt the position that the auxiliary field A is independent of the space-time metric [J. Alexandre and P. Pasipoularides, Phys. Rev. D 83, 084030 (2011).][J. Greenwald, V. H. Satheeshkumar, and A. Wang, J. Cosmol. Astropart. Phys. 12 (2010) 007.], and we assume, as in [A. M. da Silva, Classical Quantum Gravity 28, 055011 (2011).], that A is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit λ → 1, unless λ does not run, and has the fixed value λ = 1. Finally, we comment on the Horava and Melby-Thompson approach [E Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).] in which A is assumed as a part of the space-time metric in the IR. [ABSTRACT FROM AUTHOR]

We study the most general case of spherically symmetric vacuum solutions in the framework of the covanant Horava-Lifshitz gravity, for an action that includes all possible higher order terms in curvature which are compatible with power-counting normalizability requirement. We find that solutions can be separated into two main classes: (i) solutions with nonzero radial shift function, and (ii) solutions with zero radial shift function. In the case (ii), spherically symmetric solutions are consistent with observations if we adopt the view of Horava and Melby-Tomson [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010)1, according to which the auxiliary field A can be considered as a part of an effective general relativistic metric, which is valid only in the IR limit. On the other hand, in the case (i), consistency with observations implies that the field A should be independent of the spacetime geometry, as the Newtonian potential arises from the nonzero radial shift function. Also, our aim in this paper is to discuss and compare these two alternative but different assumptions for the auxiliary field A. [ABSTRACT FROM AUTHOR]

The null energy condition is considered the most fundamental of the energy conditions, on which several key results, such as the singularity theorems, are based. The Casimir effect is one of the rare equilibrium mechanisms by which it is breached without invoking modified gravity or nonminimal couplings to exotic matter. In this work we propose an independent dynamical mechanism by which it is violated, with the only ingredients being standard (but nonperturbative) quantum field theory and a minimally coupled scalar field in a double-well potential. As for the Casimir effect, we explain why the averaged null energy condition is not violated by this mechanism. Nevertheless, the transient behavior could have profound impacts in early universe cosmology. [ABSTRACT FROM AUTHOR]

We discuss second quantization, discrete symmetry transformations, and inner products in free non-Hermitian scalar quantum field theories with PT symmetry, focusing on a prototype model of two complex scalar fields with anti-Hermitian mass mixing. Whereas the definition of the inner product is unique for theories described by Hermitian Hamiltonians, its formulation is not unique for non-Hermitian Hamiltonians. Energy eigenstates are not orthogonal with respect to the conventional Dirac inner product, so we must consider additional discrete transformations to define a positive-definite norm. We clarify the relationship between canonical-conjugate operators and introduce the additional discrete symmetry C', previously introduced for quantum-mechanical systems, and show that the C'PT inner product does yield a positive-definite norm, and hence is appropriate for defining the Fock space in non-Hermitian models with PT symmetry in terms of energy eigenstates. We also discuss similarity transformations between PT-symmetric non-Hermitian scalar quantum field theories and Hermitian theories, showing that they would require modification in the presence of interactions. As an illustration of our discussion, we compare particle mixing in a Hermitian theory and in the corresponding non-Hermitian model with PT symmetry, showing how the latter maintains unitarity and exhibits mixing between scalar and pseudoscalar bosons. [ABSTRACT FROM AUTHOR]

We formulate supersymmetric non-Hermitian quantum field theories with PT symmetry, starting with free chiral boson/fermion models and then including trilinear superpotential interactions. We consider models with both Dirac and Majorana fermions, analyzing them in terms of superfields and at the component level. We also discuss the relation between the equations of motion, the (non)invariance of the Lagrangian and the (non)conservation of the supercurrents in the two models. We exhibit a similarity transformation that maps the free-field supersymmetric PT-symmetric Dirac model to a supersymmetric Hermitian theory, but there is, in general, no corresponding similarity transformation for the Majorana model. In this model, we find generically a mass splitting between bosons and fermions, even though its construction is explicitly supersymmetric, offering a novel non-Hermitian mechanism for soft supersymmetry breaking. [ABSTRACT FROM AUTHOR]

We generalize our previous formulation of gauge-invariant PT-symmetric field theories to include models with non-Abelian symmetries and discuss the extension to such models of the Englert-Brout-Higgs-Kibble mechanism for generating masses for vector bosons. As in the Abelian case, the non-Abelian gauge fields are coupled to nonconserved currents. We present a consistent scheme for gauge fixing, demonstrating Becchi-Rouet-Stora-Tyutin invariance, and show that the particle spectrum and interactions are gauge invariant. We exhibit the masses that gauge bosons in the simplest two-doublet SU(2)×U(1) model acquire when certain scalar fields develop vacuum expectation values: they and scalar masses depend quartically on the non-Hermitian mass parameter μ. The bosonic mass spectrum differs substantially from that in a Hermitian two-doublet model. This non-Hermitian extension of the Standard Model opens a new direction for particle model building, with distinctive predictions to be explored further. [ABSTRACT FROM AUTHOR]

Setting aside anthropic arguments, there is no reason why the Universe should initially favor a net expanding phase rather than one experiencing a net contraction. However, a collapsing universe containing "normal" matter will end at a singularity in a finite time. We point out that there is a mechanism, derived from nonperturbative effects in quantum field theory in a finite volume, which may provide a bias toward expansion when the spacetime volume shrinks, by dynamically violating the null energy condition, without the need for modified gravity or exotic matter. We describe a scalar field component subjected to this nonperturbative effect in a cosmological background and consider its impact on a contracting phase. We discuss how this could dynamically generate the necessary initial conditions for inflation to get started, or form part of the mechanism for a nonsingular cosmological bounce. [ABSTRACT FROM AUTHOR]

We' present a gauge and Lorentz invariant model for the scattering of matter off magnetic poles, which justifies the presence of velocity-dependent magnetic charges as an effective description of either the behavior of monopoles in scattering with matter or their production from matter particles at colliders. Hence, in such an approach, perturbativity of the magnetic charge is ensured for relative low velocities of monopoles with respect to matter particles. The model employs a U(1)weak×U(1)strong effective gauge field theory under which electrons and monopoles (assumed to be fermions) are appropriately charged. The nonperturbative quantum effects of the strongly coupled sector of the theory lead to dressed effective couplings of the monopole/dyon with the electromagnetic photon, due to nontrivial wave-function renormalization effects. For slowly moving monopole/dyons, such effects lead to weak coupling, thus turning the bare nonperturbative magnetic charge, which is large due to the Dirac/Schwinger quantization rule, into a perturbative effective, velocity-("β")-dependent magnetic coupling. Our work thus offers formal support to previous conjectural studies, employing effective U(1)-electromagnetic gauge field theories for the description of monopole production from standard model matter, which are used in contemporary collider searches of such objects. This work necessarily pertains to composite monopoles, as seems to be the case of all known monopoles so far, that are solutions of specific particle physics models. This is a consequence of the fact that the wave-function renormalization of the (slowly moving) monopole fermion turns out to violate unitarity bounds that would characterize asymptotic elementary particle states. [ABSTRACT FROM AUTHOR]

We discuss P T -symmetric Abelian gauge field theories as well as their extension to the Englert-Brout-Higgs mechanism for generating a mass for a vector boson. Gauge invariance is not straightforward, and we discuss the different related problems as well as a solution which consists in coupling the gauge field to a current that is not conserved. Non-Hermiticity then necessarily precludes the Lorenz gauge condition but nevertheless allows for a consistent formulation of the theory. We therefore generalize the Englert-Brout-Higgs mechanism to P T -symmetric field theories, opening the way to constructing non-Hermitian extensions of the Standard Model and new scenarios for particle model building. [ABSTRACT FROM AUTHOR]

We demonstrate the extension to parity-time (PT)-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimization of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantization of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels. [ABSTRACT FROM AUTHOR]

Motivated by neutrino astronomy, we consider a plane wave of coupled and massive flavors, scattered by a static black hole, and describe analytically and numerically the corresponding oscillation probability in the surrounding space. Both the interpretation as particles traveling along geodesics and as scattered waves are studied, and consistently show a nontrivial and potentially long range interference pattern, in contrast to the spatially uniform transition probability in a flat spacetime. We introduce a numerical method for studying the oscillations around black holes, which accounts for the full curved geometry and flavor wave mixing. Whilst limited to the region immediately around the black hole, this numerical approach has the potential to be used in more general contexts, revealing the complex interference patterns which defy analytic methods. [ABSTRACT FROM AUTHOR]

Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of PT-symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether's theorem, and we give specific examples for illustration. [ABSTRACT FROM AUTHOR]

We study consequences of Lorentz symmetry violation in a z=2 Lifshitz extension of QED in 3+1 dimensions, and we discuss nontrivial effects of quantization. Because of the specific power of space momentum in propagators of the model, dimensional regularization leads to an unusual interpretation of loop integrals, which are finite even when the space dimension goes to the integer 3. We check the consistency of the approach by calculating the (vanishing) corrections to the photon mass and the IR-divergence-free corrections to the dispersion relation for massless fermions. [ABSTRACT FROM AUTHOR]