Space-time structure of weak and electromagnetic interactions

The generator of electromagnetic gauge transformations in the Dirac equation has a unique geometric interpretation and a unique extension to the generators of the gauge group SU(2) × U(1) for the Weinberg-Salam theory of weak and electromagnetic interactions. It follows that internal symmetries of the weak interactions can be interpreted as space-time symmetries of spinor fields in the Dirac algebra. The possibilities for interpreting strong interaction symmetries in a similar way are highly restricted.     

Dynamical symmetry breaking in SO(4n+2) and E(6) gauge theories

We find that SO(4n+2) and E(6) gauge theories with fermions in the complex spinor representation (and no scalar fields at all) undergo dynamical breaking of the gauge symmetry, according to the rules of Raby, Dimopoulos, and Susskind.     

Derivation of an effective Lagrangian from a generalized scalar curvature

A spinor Lagrangian invariant under global coordinate, local Lorentz and local chiral SU(n) × SU(n) gauge transformations is presented. The invariance requirement necessitates the introduction of boson fields, and a theory for these fields is then developed by relating them to generalizations of the vector connections in general relativity and utilizing an expanded scalar curvature as a boson Lagrangian. In implementing this plan, the local Lorentz group is found to greatly facilitate the correlation of the boson fields occurring in the spinor Lagrangian with the generalized vector connections.The independent boson fields of the theory are assumed to be the inhomogeneously transforming irreducible parts of the connections. It turns out that no homogeneously transforming parts are necessary to reproduce the chiral Lagrangian usually used as a basis for phenomenological field theories. The Lagrangian in question appears when the gravitational interaction is turned off. It includes pseudoscalar, spinor, vector, and axial vector fields, and the vector fields carry mass in spite of the fact that the theory is locally gauge invariant.     

A scaling limit with many noncommutativity parameters

We derive the worldsheet propagator for an open string with different magnetic fields at the two ends, and use it to compute two distinct noncommutativity parameters, one at each end of the string. The usual scaling limit that leads to noncommutative Yang–Mills can be generalized to a scaling limit in which both noncommutativity parameters enter. This corresponds to expanding a theory with U(N) Chan–Paton factors around a background U(1)^N gauge field with different magnetic fields in each U(1).     

Baryon-antibaryon asymmetry in a model with domain structure and soft CP violation

We consider a model with an abelian gauge symmetry, a Higgs potential involving two scalar fields, and two spinor fields coupled to the scalars through Yukawa couplings. The model accomodates soft violation of charge conjugation, and a domain structure of the universe with two different types of domains, which have identical energy but are governed by different effective lagrangians. The effective lagrangian has complex c-number coefficients that become parts of effective coupling constants, and these are different in the two kinds of domains. In spite of that fact the model neither predicts any domain-dependent effects, nor any particle-antiparticle asymmetries within domains.     

Point-splitting derivation of anomalous divergence for the spinor current

The anomaly for the divergence of the spinor current in the supersymmetric Yang-Mills theory is obtained by the point-splitting regularization method. The results agree with those of the lowest order perturbation theory. The anomaly is removed by redifinition of the gauge invariant conserved current.     

On the geometrization of matter by exotic smoothness

In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein–Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and leading to a Dirac term in the Einstein–Hilbert action. For sufficient complicated links and knots, there are “connecting tubes” (graph manifolds, torus bundles) which introduce an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components. We also discuss the gauge group of the theory to be U(1) × SU(2) ×?SU(3).     

Calculation of gauge couplings and compact circumferences from self-consistent dimensional reduction

We consider a system of gravity plus free massless matter fields in 4 + N dimensions, and look for solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields. For manifolds of sufficient symmetry (including spheres, CP^N, and manifolds of simple Lie groups) the metric depends on only a single multiplicative parameter ?², and the field equations reduce to an algebraic equation for ?, involving the potential of the matter fields in the metric of the manifold. With a large number of species of matter fields, the manifold will be larger than the Planck length, and the potential can be calculated using just one-loop graphs. In odd dimensions these are finite, and give a potential of form C_N/?⁴. Also there are induced Yang-Mills and Einstein-Hilbert terms in the effective 4-dimensional action, proportional to additional numerical coefficients, D_N and E_N. General formulas are given for the gauge coupling g² in terms of C_N and D_N, and the ratio ?²/8πG in terms of C_N and E_N. Numerical values for C_N, D_N, and E_N are obtained for scalar and spinor fields on spheres of odd dimensionality N. It is found that the potential, g² and ?²/8πG can all be positive but only when the compact manifold has N = 3 + 4 k dimensions. (The positivity of the potential is needed for stability of the sphere against uniform dilations or contractions). In this case, solutions exist either for spinor fields alone or for suitable mixes of spinor and scalar fields provided the ratio of the number of scalar fields to the number of fermion fields is not too large. Numerical values of the O(N + 1) gauge couplings and 8φG/?² are calculated for illustrative values of the numbers of spinor fields. It turns out that large numbers of matter fields are needed to make these parameters reasonably small.     

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U (n). As the result, one can create a theory of particle evolution that is gauge-invariant with regards to the group Uⁿ (1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U (1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping, and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory, the article considers a number of important particular examples, both known and new.     

The anomalous 3-boson couplings as an implication of the Higgs sector

We discuss the possible new electroweak interactions which may be generated by the Higgs sector at the scale of theZ mass. For this purpose, we give a set ofSU(2)×U(1) gauge invariant operators constructed in terms ofW, Z, γ and Higgs fields which in the unitary gauge describe all possible γWW andZWW anomalous couplings. The dimension of these operators varies from 6 to 12. This fact allows us to consider various scenaria for the manifestations of the New Physics. We conclude that the underlying dynamics induced by the Higgs sector can be tested through a model-independent amplitude analysis of gauge boson pair production at LEP2 and future colliders.     

Embedding Z′ models in SO(10) GUTs

We embed a theory with Z′ gauge boson (related to an extra U(1) gauge group) into a supersymmetric GUT theory based on SO(10). Two possible sequences of SO(10) breaking via VEVs of appropriate Higgs fields are considered. Gauge coupling unification provides constraints on the low energy values of two additional gauge coupling constants related to Z′ interactions with fermions. Our main purpose is to investigate in detail the freedom in these two values due to different scales of subsequent SO(10) breaking and unknown threshold mass corrections in the gauge RGEs. These corrections are mainly generated by Higgs representations and can be large because of the large dimensions of these representations. To account for many free mass parameters, effective threshold mass corrections have been introduced. Analytic results that show the allowed regions of values of two additional gauge coupling constants have been derived at 1-loop level. For a few points in parameter-space that belong to one of these allowed regions 1-loop running of gauge coupling constants has been compared with more precise running, which is 2-loop for gauge coupling constants and 1-loop for Yukawa coupling constants. 1-loop results have been compared with experimental constraints from electroweak precision tests and from the most recent LHC data.     

Grand unification in RS1

We study unification in the Randall-Sundrum scenario for solving the hierarchy problem, with gauge fields and fermions in the bulk. We calculate the one-loop corrected low-energy effective gauge couplings in a unified theory, broken at the scale M_GUT in the bulk. We find that, although this scenario has an extra dimension, there is a robust (calculable in the effective field theory) logarithmic dependence on M_GUT, strongly suggestive of high-scale unification, very much as in the (4D) Standard Model. Moreover, bulk threshold effects are naturally small, but volume-enhanced, so that we can accommodate the measured gauge couplings. We show in detail how excessive proton decay is forbidden by an extra U(1) bulk gauge symmetry. This mechanism requires us to further break the unified group using boundary conditions. A 4D dual interpretation, in the sense of the AdS/CFT correspondence, is provided for all our results. Our results show that an attractive unification mechanism can combine with a non-supersymmetric solution to the hierarchy problem.     

Low-scale axion from large extra dimensions

The mass of the axion and its decay rate are known to depend only on the scale of Peccei–Quinn symmetry breaking, which is constrained by astrophysics and cosmology to be between 10⁹ and 10¹² GeV. We propose a new mechanism such that this effective scale is preserved and yet the fundamental breaking scale of U(1)_PQ is very small (a kind of inverse seesaw) in the context of large extra dimensions with an anomalous U(1) gauge symmetry in our brane. The production and decay of the associated Z_A gauge boson, which ends up as two gluons and two axions, is a distinct collider signature of this scenario.     

CONFINEMENT PROPERTIES OF THE PURE GAUGE FIELDS ON COSET SPACE OF AN ABELIAN CHIRAL GROUP

In this paper the lattice current-current propagator is calculated and the influence of coset pure gauge fields of an Abelian chiral group G=U₁×U⁵ on confinement properties of a quark system is discussed by virtue of the Wilson's criterion of lattice gauge theory. When subgroup H is U₁, the coset pure gauge fields only contribute a perimeter law factor to the current-current propagator which has no influence on confinement properties of the system. When subgroup H is U⁵, the coset pure gauge fields also have no influence on confinement properties of the system.     

Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an U(1) Gauge Field

Light-front quantization of the conformally gauge-fixed Polyakov D1 brane action in the presence of a constant background scalar axion field C(τ, σ) and an U(1) gauge field A _α (τ, σ) is studied. The axion field C and the U(1) gauge field A _α , are seen to behave like the Wess–Zumino (WZ) fields and the term involving these fields is seen to behave like a WZ term for this action.     

Is hypercharge U(1) in Weinberg's model redundant?

The U₁ × U₁(loc) × SU₂(loc) invariant Weinberg lagrangian can be reduced to a U₁ × SU₂(loc) invariant lagrangian without hypercharge group involving only a single left-handed Weyl spinor field and an isotriplet gauge vector field. Spontaneous symmetry breakdown is induced by condensation of fermion pairs. Charge appears simply as “isospin charge”.     

Energy levels of QED in a Euclidean formulation

Hydrogen-like energy levels of scalar and spinor QED are calculated using a Euclidean functional approach. The matter field is integrated over. Stationary points of the resulting effective action already yield a hydrogen like level structure for the energy. There is an interesting difference between the scalar and the spinor case. Whereas for spinors the conventional results are reproduced, the calculation for scalars yields a fine structure which is opposite in sign to the conventional one and has no critical singularity at Zα=1/2. The crucial structural difference between the two cases is that, for scalars, minima for the gauge invariant energy are not extrema of the action, even for time independent fields.