Fermionic Symmetry Research Articles

The origin of Siegel symmetry in superstrings

The sigma model interpretation of superstrings is studied. It is shown that additional local fermionic symmetries in these models are a consequence of the degeneracy of the Cartan metric and the fact that the structure constants of the supersymmetry algebra form a Clifford algebra.

Quantization of N=1,2 superparticle with irreducible constraints

An action for the D=10 superparticle with N=1.2 suppersymmetry, containing irreducible (functionally indepndent) Lorentz covariant constraints only, is proposed. The key ingredient is the enlargening of the usual superspace to include additional bosonic harmonic coordinates which transform as Lorentz spinors and are pure gauge degrees of freedom. Upon quantization the extended superparticle provides a Lorentz covariant on-shell description of the linearized D=10 type IIb supergravity. The first-quantized BRST charge contains a multighost interaction term which is inevitable when the functional dependence of the reparametrization and the local fermionic symmetry constraints is correctly taken into account.

Superspace supergravity from the superstring

We study a classical superstring propagating in a “curved” (10,16)-dimensional superspace. In this formulation of the string, a local fermionic symmetry is needed to eliminate ghosts from the particle spectrum. By studying the constraint algebra, we show that any background field configuration consistent with this symmetry is equivalent to one which satisfies the full set of supergravity equations.

Irreducible representations of the staggered fermion symmetry group

In this paper a method is presented to obtain all the irreducible representations of the symmetry group LS of the staggered fermion action. This group has the structure of a four-dimensional space group, but for the shifts (translations), which anticommute. It is shown how the irreducible representations of the rest frame symmetry group (containing symmetries of the transfer matrix) can be obtained upon reduction of irreducible representations of LS.

Supergravity torsion constraints from the 10D superparticle

The classical superparticle propagating in a curved superspace is studied. Requiring that there be a local fermionic symmetry imposes restrictions on the background. The equivalence relation among background superfields which is implied by the superparticle dynamics is discussed, and it is shown that up to such equivalences the torsion superfields obey the supergravity constraints.

Finiteness of Ricci flatN=2 supersymmetric σ-models

We study the ultraviolet behavior of two dimensional supersymmetric non-linear σ-models with target space an arbitrary Kahler manifoldM, so that the models areN=2 supersymmetric. We point out that these models have an additional fermionic axial symmetry if and only if the metric onM is Ricci flat. We show that the preservation of this symmetry in perturbation theory implies that both bare and renormalized metrics onM are Ricci flat. Combining this result with the constraint ofN=2 supersymmetry requiring that all counter-terms to the metric beyond one-loop order be cohomologically trivial, we argue thatN=2 models defined on Ricci flat Kahler manifolds are on-shell ultraviolet finite to all orders of perturbation theory.

Matter coupled to D=2 simple unidexterous supergravity, local (supersymmetry)2 and strings

The authors use previously derived results to write an action which describes the coupling of a set of string coordinates to simple unidexterous world-sheet supergravity. They demonstrate the presence of the fermionic symmetry that implies decoupling of unphysical string states, even when local (1,0) supersymmetry is realised on the world sheet of the string.

Superstring propagation in curved superspace in the presence of background super Yang-Mills fields

A gauge invariant action is presented which describes the propagation of the superstring in curved superspace in the presence of background super Yang-Mills fields. It is shown that this action posseses the local fermionic world-sheet symmetry needed for a consistent coupling of the string to background fields. Some other aspects of the superspace non-linear σ-model described by this action are also discussed.

Relation between the interacting boson-fermion approximation model and dynamical boson-fermion symmetries.

The relation between the phenomenological Hamiltonian as used in dynamical boson-fermion symmetries and the semimicroscopic Hamiltonian of the interacting boson-fermion approximation, both used in the description of odd-mass nuclei, is studied in detail. Predictions are obtained for the parameters of the boson fermion symmetry Hamiltonian. From the microscopic picture behind the interacting boson-fermion approximation model, predictions are also obtained for the regions in the table of isotopes where the boson-fermion symmetries can be expected to occur. In addition we derive the structure of an additional exchange force, which results from the interaction between like particles.

Comment on "Quantum effects on four-dimensional space-time symmetries"

It is noted that there is no anomaly in the Lorentz symmetry of charged chiral fermions.(AIP)

Precocious unification in simple grand unified theories.

We investigate how simple grand unified theories with a precocious-unification mass can be constructed. The maximal local symmetry of 2mn left-handed fermions and their left-handed antiparticles is shown to be a viable candidate, where m and n are the number of families and colors, respectively. The predictions of such a model are studied.

Fermion mass generation and electroweak symmetry breaking from colour forces

The colour gauge group is extended to SU(3) ⊗ SU(3) and is subsequently broken to diagonal SU(3) c. Under the diagonal SU(3) c the fundamental fermionic constituents of the larger strong group become ordinary quarks plus new quarks with exotic quantum numbers. Chiral symmetry breaking in the exotic quark sector may occur at much larger mass scales than ordinary chiral symmetry breaking, and could produce dynamical breaking of electroweak gauge symmetry and radiative masses for the light fermions.

On a self-consistent chiral doublet composite scheme

A composite scheme with a chiral doublet of charges Q=( 2 3 , − 1 3 ) is considered. The scheme is self-consistent in the sense that the constituent spectator chiral symmetry SE(2) × U(1) coincides with the chiral electroweak symmetry. Due to the mirror fermions they both are anomaly free. The chiral colour symmetry arises as an effective symmetry of composite quarks. The scheme contains exotic composite fermions with isospin I= 3 2 . The common maximal effective symmetry of both ordinary and exotic composite fermions is the chiral SU(2) × SU(4) one, the latter being a possible partial unified symmetry.

Low-energy restoration of parity and maximal symmetry

The maximal symmetry of fermions of one generation, SU(16), which includes the left-right-symmetric Pati-Salam group, $\mathrm{SU}{(4)}_{c}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}$, as a subgroup, allows the possibility of a low-energy (${M}_{R}\ensuremath{\sim}100$ GeV) breaking of the left-right symmetry. It is known that such a low-energy restoration of parity can be consistent with weak-interaction phenomenology. We examine different chains of descent of SU(16) that admit a low value of ${M}_{R}$ and determine the other intermediate symmetry-breaking mass scales associated with each of these chains. These additional mass scales provide an alternative to the "great desert" expected in some grand unifying models. The contributions of the Higgs fields in the renormalization-group equations are retained and are found to be important.