Gauge symmetry as symmetry of matrix coordinates

We propose a new point of view on gauge theories, based on taking the action of symmetry transformations directly on the space coordinates. Via this approach the gauge fields are not introduced at the first step, and they can be interpreted as fluctuations around some classical solutions of the model. The new point of view is connected to the lattice formulation of gauge theories, and the parameter of the non-commutativity of the coordinates appears as the lattice spacing parameter. Through the statements concerning the continuum limit of lattice gauge theories, the suggestion arises that the non-commutative spaces are the natural ones to formulate gauge theories at strong coupling. Via this point of view, a close relation between the large-N limit of gauge theories and string theory can be made manifest. Received: 16 June 2000 / Published online: 8 September 2000     

Renormalization and symmetry conditions in supersymmetric QED

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov–Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms. Received: 23 July 1999 / Published online: 14 October 1999     

Internal symmetry currents and supersymmetric effective lagrangians

A supersymmetric and non-linearly realized internally symmetric action is constructed from the super Kähler potential of Goldstone scalar superfields. Noether's theorem in superspace is derived and the associated superfield of currents defined. The currents are used to derive a super Dashen formula relating the (quasi) Goldstone masses and decay constants to the symmetry breaking part of the theory and to supersymmetrically gauge the invariant subgroup as well as the full group.     

Radiative symmetry breaking in supersymmetric models

We propose a scheme where the three relevant physics scales related to the supersymmetry, electroweak, and baryon minus lepton (B−L) breakings are linked together and occur at the TeV scale. The phenomenological implications in the Higgs and leptonic sectors are discussed.     

Gauge invariance of relativistic two-particle bound-state energies (I)

The gauge invariance of relativistic two-particle energy levels in quantum electrodynamics is demonstrated for both covariant and non-covariant gauges, by considering infinitesimal gauge transformations from a fixed gauge. The proof is carried out by expressing the bound-state energies in terms of ratios of contour integrals involving four-point Green functions in the neighborhood of their poles in the energy plane. The generalized Ward-Takahashi identities are then used to help reduce the Green functions which appear into forms which make the singularity structure of the four-point function apparent. The formalism is illustrated for the special cases of one- and two-photon exchange in perturbation theory.     

Gauge symmetry and the EMC spin effect

We emphasise the EMC spin effect as a problem of symmetry and discuss the renormalisation of theC=+1 axial tensor operators. This involves the generalisation of the Adler-Bell-Jackiw anomaly to each of these operators. We find that the contribution of the axial anomaly to the spin dependent structure functiong ₁(x, Q ²) scales at O(α_s). This means that the anomaly can be a largex effect ing ₁. Finally we discuss the jet signature of the anomaly.     

Gauge internal symmetry in extended supergravity

Extended supergravity theories with global O(2) and SO(3) internal symmetry have recently been constructed, and a mechanism which implements local O(2) and SO(3) gauge invariance is given here. The introduction of a minimal gauge coupling automatically leads to a $\text{spin}\text{-}\text{3}\text{2}$ mass and a cosmological term in order to preserve local supersymmetry. Local internal symmetry for a $\text{spin}\text{-}\text{3}\text{2}$ field is related to spontaneous breakdown of global supersymmetry. Perturbation theory results which confirm the physical consistency of the system are given.     

Gauge symmetry breaking in matrix models

We argue that some features of the standard model, in particular the fermion assignment and symmetry breaking, can be obtained in matrix model which describes noncommutative gauge theory as well as gravity in an emergent way. The mechanism is based on the presence of some extra (matrix) dimensions. These extra dimensions are different from the usual ones which give to a noncommutative geometry of the Grönewold-Moyal type, and are reminiscent of the Connes-Lott model, although the action is very different.     

Gauge coupling unification in the exceptional supersymmetric Standard Model

We consider the renormalisation group flow of gauge couplings within the so-called exceptional supersymmetric Standard Model (E₆SSM) based on the low-energy matter content of 27-dimensional representations of the gauge group E₆$E_6$, together with two additional non-Higgs doublets. The two-loop beta functions are computed, and the threshold corrections are studied in the E₆SSM. Our results show that gauge coupling unification in the E₆SSM can be achieved for phenomenologically acceptable values of α₃(MZ)${\alpha }_3(M_Z)$, consistent with the central measured low-energy value, unlike in the minimal supersymmetric Standard Model (MSSM) which, ignoring the effects of high energy threshold corrections, requires significantly higher values of α₃(MZ)${\alpha }_3(M_Z)$, well above the experimentally measured central value.     

Patterns of symmetry breaking in supersymmetric gauge theories

We give a group-theoretical analysis of the spontaneous breaking of the gauge group in supersymmetric Yang-Mills theories with unbroken supersymmetry.     

Random Neural Network with Local Gauge symmetry

Here we propose that the model of random surfaces coupling with spins in a local gauge symmetric manner may be closely related with the biological neural networks. We argue that the local gauge symmetry is a rather general requirement for the neural network models.     

Gauge symmetry and supersymmetry in the Higgsless standard model

The group SO(6) ⊗ SO(5) is shown to be the gauge group as well as supersymmetry group of a four dimensional superstring model. Here, we discuss how supersymmetry is realised in 4-dimensions and further, we successfully reproduce the gauge symmetry results. Using the SO(6) ⊗ SO(5) group, all the known aspects of the string theory are obtained. The model reduces to the Standard Model which has the capability of containing the ingredients of a successful theory of the present day physics. However, there are no Higgs in the model.     

Gauge invariance and spontaneous symmetry breaking in two-gap superconductors

The gauge symmetry of the Ginzburg–Landau theory for two-gap superconductors is analyzed in this letter. We argue that the existence of two different phases, associated with the two independent scalar Higgs fields, explicitly breaks the gauge symmetry of the Ginzburg–Landau Hamiltonian, unless a new additional vector field is included. Furthermore, the interference term, or Josephson coupling, holding a direct dependence with the phase difference, also explicitly breaks down the gauge symmetry. We show that a solution for the problem is achieved by adding an additional kinetic coupling term between the two vector fields, which generates the desired terms through a spontaneous symmetry breaking mechanism. Finally, the electrodynamics of the system is also presented in terms of the supercurrents inside the superconducting region.     

Gauge fields,BRS symmetry and the Casimir effect

The canonical quantization of the photon field in covariant gauge is studied in the presence of static boundaries, on which the field satisfies either “bag” or superconductor boundary conditions. The inclusion of the Fadeev-Popov ghost fields is found to be essential for agreement with Coulomb gauge calculations of the Casimir energy.