Isovector Scalar Field Research Articles

Super-exceptional embedding construction of the heterotic M5: Emergence of SU(2)-flavor sector

A new super-exceptional embedding construction of the heterotic M5-brane's sigma-model was recently shown to produce, at leading order in the super-exceptional vielbein components, the super-Nambu-Goto (Green-Schwarz-type) Lagrangian for the embedding fields plus the Perry-Schwarz Lagrangian for the free abelian self-dual higher gauge field. Beyond that, further fields and interactions emerge in the model, arising from probe M2- and probe M5-brane wrapping modes. Here we classify the full super-exceptional field content and work out some of its characteristic interactions from the rich super-exceptional Lagrangian of the model. We show that SU(2)×U(1)-valued scalar and vector fields emerge from probe M2- and M5-branes wrapping the vanishing cycle in the A1-type singularity; together with a pair of spinor fields of U(1)-hypercharge ±1 and each transforming as SU(2) iso-doublets. Then we highlight the appearance of a WZW-type term in the super-exceptional PS-Lagrangian and find that on the electromagnetic field it gives the first-order non-linear DBI-correction, while on the iso-vector scalar field it has the form characteristic of the coupling of vector mesons to pions via the Skyrme baryon current. We discuss how this is suggestive of a form of SU(2)-flavor chiral hadrodynamics emerging on the single (N=1) M5 brane, different from, but akin to, holographic large-N QCD.

Scalar hairy black holes and solitons in a gravitating Goldstone model

We study black hole solutions of Einstein gravity coupled to a specific global symmetry breaking Goldstone model described by an O(3) isovector scalar field in four spacetime dimensions. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. A set of globally regular, particle-like solutions are found in the limit of vanishing event horizon radius. These configurations can be viewed as ‘regularised’ global monopoles, since their mass is finite and the spacetime geometry has no deficit angle. As an unusual feature, we notice the existence of extremal black holes in this model defined in terms of gravity and scalar fields only.

Isovector Scalar Field Effects in Asymmetric Nuclear Matter

Density-dependent parametrization models of the nucleon-meson coupling constants, including the isovector scalar δ-field, are applied to asymmetric nuclear matter. The nuclear equation of state (EOS) and the neutron star properties are studied in a relativistic Lagrangian density, using the relativistic mean field (RMF) hadron theory. It is known that the δ-field in the constant coupling scheme leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses, finally influences the stability of the neutron stars. We use density-dependent models of the nucleon-meson couplings to study the properties of neutron star matter and to reexamine the δ-field effects in asymmetric nuclear matter. Our calculation shows that the stability conditions of the neutron star matter can be improved in presence of the δ-meson in the density-dependent models of the coupling constants. The EOS of nuclear matter strongly depends on the density dependence of the interactions.

Goldstone models in D + 1 dimensions, D = 3, 4, 5, supporting stable and zero topological charge solutions

We study finite energy static solutions to a global symmetry breaking Goldstone model described by an isovector scalar field in D + 1 spacetime dimensions. Both topologically stable multisolitons with arbitrary winding numbers and zero topological charge soliton–antisoliton solutions are constructed numerically in D = 3, 4, 5. We have explored the types of symmetries the systems should be subjected to, for there to exist multisoliton and soliton–antisoliton pairs in D = 3, 4, 5, 6. These findings are underpinned by constructing numerical solutions in the D ⩽ 5 examples. Subject to axial symmetry, only multisolitons of all topological charges exist in even D, and in odd D only zero and unit topological charge solutions exist. Subjecting the system to weaker than axial symmetries results in the existence of all the possibilities in all dimensions. Our findings also apply to finite ‘energy’ solutions to Yang–Mills and Yang–Mills–Higgs systems as well as to sigma models, but we find the numerical work for the Goldstone models more accessible.

Solitons and soliton–antisoliton pairs of a goldstone model in 3 + 1 dimensions

We study finite energy static solutions to a global symmetry breaking model in 3+1 dimensions described by an isovector scalar field. The basic features of two different types of configurations are discussed, one of them corresponding to axially symmetric multisolitons with topological charge $n$, and the other one to unstable soliton-antisoliton pairs with zero topological charge.

Berry phase and induced fractional fermion number on vaccum

We show that, in four dimensional field-theoretical model containing fermion field and background isovector scalar field, an induced magnetic monopole field emerges as a result of adiabatical evolution of the scalar field. For the corresponding Dirac Hamiltonian the degenerate eigenmodes of the vacuum are known to exist. The effective system is then shown to give fractional fermion number on vacuum. In the present approach the magnetic monopole field is not quite essentially given as a topologically non-trivial external field but induced as the result of adiabatic evolution of a scalar field.

Baryon QCD sum rules in an external isovector-scalar field and baryon isospin mass splittings.

Within the QCD sum-rule approach in an external field, we calculate the baryon matrix element of isovector-scalar current, $H_{\rm B}=\langle B|\overline{u}u- \overline{d}d|B\rangle/2M_{\rm B}$, for octet baryons, which appears in the response of the correlator of baryon interpolating fields to a constant isovector-scalar external field. The sum rules are obtained for a general baryon interpolating field with an appropriate form for the phenomenological ansatz of the spectral density. The key phenomenological input is the response of the quark condensates to the external field. To first order in the quark mass difference $\delta m=m_d-m_u$, the non-electromagnetic part of the baryon isospin mass splitting is given by the product of $\delta m$ and $H_{\rm B}$. Therefore, QCD sum-rule calculation of $H_{\rm B}$ leads to an estimate of the octet baryon isospin mass splittings. The resulting values are comparable to the experimental values; however, the sum-rule predictions for $H_{\rm B}$ are sensitive to the values of the response of the quark condensates to the external source, which are not well determined.

The no-scale non-linear sigma model, magnetic charge, the cosmological constant, compactification and symmetry breaking

`No-scale non-linear sigma models' are considered in three-, four-, and six-dimensional spacetimes. These are theories with global gauge invariance, which here we take to be SO(3) or SL(3,R) and where a homogeneous non-linear constraint is imposed. In contrast with the more standard non-linear sigma model, this constraint does not determine a particular scale for the strength of the isovector scalar field. In three dimensions, a version of the model is totally equivalent to ordinary electrodynamics, while the generalization of this model to 3+1 dimensions leads to a version of relativistic magnetohydrodynamics. Still in 3+1 dimensions, the constraint in terms of a field strength, which in turn is defined in terms of the fundamental scalars, defines a coupling of this field strength to a magnetic source. In this model we also obtain an additional vector U(1) local gauge invariance associated with this magnetic charge. In six dimensions the minimal magnetic coupling to fundamental membranes appears naturally. In six dimensions, it is possible to obtain a compactification of two dimensions into a sphere by the presence of a hedgehog configuration of the isovector scalar field, with the resulting four-dimensional effective cosmological constant being zero. A mechanism is discussed for generating breaking of the gauge symmetry, induced by SL(3,R) breaking terms, at a scale much smaller than the Planck scale. The SL(3,R) symmetry is expected to protect this hierarchy. Also, no massless-`moduli' scalar fields remain after compactification.

Calculation of from QCD sum rules and the neutron-proton mass difference.

The proton matrix element of the isovector-scalar density, $<p|\overline{u}u-\overline{d}d|p>/2M_p$, is calculated by evaluating the nucleon current correlation function in an external isovector-scalar field using the QCD sum-rule method. In addition to the usual chiral and gluon condensates of the QCD vacuum, the response of the chiral condensates to the external isovector field enters the calculation. The latter is determined by two independent methods. One relates it to the difference between the up and down quark chiral condensates and the other uses the chiral perturbation theory. To first order in the quark mass difference $\delta m=m_d-m_u$, the non-electromagnetic part of the neutron-proton mass difference is given by the product $\delta m <p|\overline{u}u-\overline{d}d|p>/2M_p$; the resulting value is in reasonable agreement with the experimental value.

No scale nonlinear sigma model, hedgehog compactification, and the cosmological constant.

The no scale nonlinear [sigma] model'' is a six-dimensional (6D) Kaluza-Klein model containing an isovector scalar field whose dynamics has global SO(3) invariance and where a homogeneous nonlinear constraint is imposed. In contrast with the more standard nonlinear [sigma] model, this constraint does not determine a particular scale for the strength of the isovector scalar field. In this model we study a mechanism for the compactification of two dimensions into a sphere by the presence of a hedgehog configuration of the isovector scalar field. Consistency with the gravitational (Einstein's for [ital D]=6) equations forces the strength of the hedgehog to be the Planck scale. The resulting 4D effective cosmological constant is zero if the 6D cosmological constant is also zero, without the need of fine-tuning parameters in the Lagrangian.