Hyper-Hermitian metrics with symmetry

We show that any four-dimensional hyper-Hermitian manifold admitting a non-trivial triholomorphic Killing vector field is locally determined by the solution of a monopole-like equation on a three-dimensional Einstein-Weyl space of a special type. Conversely, any four-dimensional hyper-Hermitian manifold admitting a non-trivial tri-holomorphic Killing vector field arises in this way.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Density-metric unimodular gravity: Vacuum maximal symmetry

We have investigated the vacuum maximally symmetric solutions of recently proposed density-metric unimodular gravity theory. The results are widely different from inflationary scenario. The exponential dependence on time in deSitter space is substituted by a power law. Open space–times with non-zero cosmological constant are excluded.     

Mott insulators without symmetry breaking

We present theoretical models, in one and two space dimensions, that exhibit Mott insulating ground states at fractional occupations without any symmetry breaking. The Hamiltonians of these models are nonlocal in configuration space, but local in phase space.     

Vacuum instabilities in models with spontaneous symmetry breaking

Adopting as a reference a simple model with spontaneously broken symmetry we show that the extra massless field present in the three approximation in addition to the true Goldstone bosons may induce, through the radiative corrections to its vacuum expectation value, infrared effects which are not compensable without spoiling the symmetry itself. We further extend the analysis to generic lagrangian field models with spontaneous symmetry breaking and prove that the only constraint to their renormalizability arises from the radiative corrections to the vacuum expectation value of the massless fields, except for the true Goldstone bosons which never induce such pathologies.     

Spin-isospin mixing without spontaneous symmetry breakdown

The phenomenon advertised in the title is demonstrated in an exactly symmetricSU(2) classical gauge theory with a scalar isodoublet of matter fields. Possible implications for chromodynamics are discussed briefly.     

Warped electroweak breaking without custodial symmetry

We propose an alternative to the introduction of an extra gauge (custodial) symmetry to suppress the contribution of KK modes to the T   parameter in warped theories of electroweak breaking. The mechanism is based on a general class of warped 5D metrics and a Higgs propagating in the bulk. The metrics are nearly AdS in the UV region but depart from AdS in the IR region, towards where KK fluctuations are mainly localized, and have a singularity outside the slice between the UV and IR branes. This gravitational background is generated by a bulk stabilizing scalar field which triggers a natural solution to the hierarchy problem. Depending on the model parameters, gauge-boson KK modes can be consistent with present bounds on EWPT for mKK?1 TeV$m_{\mathit{KK}}?1\text{TeV}$ at 95% CL. The model contains a light Higgs mode which unitarizes the four-dimensional theory. The reduction in the precision observables can be traced back to a large wave function renormalization for this mode.     

Singularities in separable metrics with spherical,plane, and hyperbolic symmetry

We obtain all possible solutions to the Einstein equations for a perfect fluid with a metric of the form

The static metrics with cylindrical symmetry describing a model of cosmic strings

We discuss a set of static metrics with cylindrical symmetry describing the interior and exterior space-time of a model of cosmic strings considered recently in cosmology. The interior metric depends on one arbitrary function and the exterior on one constant. We find the relation between this constant and the linear mass density of the cosmic string. A cosmic string can be also treated as a line source in the framework of the distribution-valued curvature formalism which allows us to obtain again the same relation.     

Higgs phenomenon without symmetry breaking order parameter

We discuss symmetry-breaking order parameters, e.g. 〈?〉, in gauge theories with Higgs scalars, ?, in suitable gauges. We show that, typically, 〈?〉 = 0. A complete set of gauge-invariant, observable composite fields for such theories, local ones and ones localized near strings (paths) is constructed. We then examine the validity of standard perturbation theory, based on assuming that 〈?〉 ≠ 0, and reformulate it in terms of our gauge-invariant fields and without assuming that 〈?〉 ≠ 0. Finally, we classify classical field configurations with non-trivial topology (“defects”) in such theories and propose a defect-gas approach to predict their effects.     

Real non-Hermitian energy spectra without any symmetry

Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones are constrained by symmetries such as PT-symmetry, which is incompatible with realizing some of the most exotic non-Hermitian phenomena. In this work, we investigate how the non-Hermitian skin effect provides an alternative route towards enforcing real spectra and system stability. We showcase, for different classes of energy dispersions, various ansatz models that possess large parameter space regions with real spectra, despite not having any obvious symmetry. These minimal local models can be quickly implemented in non-reciprocal experimental setups such as electrical circuits with operational amplifiers.     

Brane world cosmology without the Z2 symmetry

The Friedmann equation for a positive tension brane situated between two bulk spacetimes that posses the same 5D cosmological constant, but which does not posses a Z₂ symmetry of the metric itself is derived, and the possible effects of dropping the Z₂ symmetry on the expansion of our Universe are examined; cosmological constraints are discussed. We show the effect of this is an inflation-like period at very early times. The global solutions for the metric in the infinite extra dimension case are found and comparison with the symmetric case is made. We show that any brane world senario of this type must revert to a Z₂ symmetric form at late times, and hence rule out certain proposed scenarios.     

Solutions of five-dimensional general relativity without spatial symmetry

Conformastationary solutions of the five-dimensional vacuum Einstein equations, depending on one or two harmonic potentials, are constructed. The solutions depending on one potential fall in three distinct classes. Solutions of two of these classes may be combined to yield a class of solutions depending on two potentials, which correspond to the Israel-Wilson-Perjès solutions of the Einstein-Maxwell theory. The asymptotically flat solutions of this class describe systems of rotating electric or magnetic monopoles.