Terms Of Gauge Fields Research Articles

"SCHWINGER MODEL" ON THE FUZZY SPHERE

In this paper, we construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this "Schwinger model". In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator Dq on the q-deformed fuzzy sphere [Formula: see text] is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators Dq and D alone. Using the path integral method, we have calculated the 2n-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.

BAGS AND CONFINEMENT GOVERNED BY SPONTANEOUS SYMMETRY BREAKING OF SCALE INVARIANCE

A general coordinate invariant theory is constructed where confinement of gauge fields and gauge dynamics in general is governed by the spontaneous symmetry breaking (s.s.b.) of scale invariance. The model uses two measures of integration in the action, the standard [Formula: see text] where g is the determinant of the metric and another measure Φ independent of the metric. To implement scale invariance, a dilaton field is introduced. Using the first-order formalism, curvature (ΦR and [Formula: see text]) terms, gauge field term ([Formula: see text] and [Formula: see text]) and dilaton kinetic terms are introduced in a conformally invariant way. Exponential potentials for the dilaton break down (softly) the conformal invariance down to global scale invariance, which also suffers s.s.b. after integrating the equations of motion. The model has a well-defined flat space limit. As a result of the s.s.b. of scale invariance phases with different vacuum energy density appear. Inside the bags, that is in the regions of larger vacuum energy density, the gauge dynamics is normal, that is nonconfining, while for the region of smaller vacuum energy density, the gauge field dynamics is confining. Likewise, the dynamics of scalars, like would be Goldstone bosons, is suppressed inside the bags.

QUANTIZATION OF CHIRAL ANTISYMMETRIC TENSOR FIELDS

Chiral antisymmetric tensor fields can have chiral couplings to quarks and leptons. Their kinetic terms do not mix different representations of the Lorentz symmetry and a local mass term can be forbidden by symmetry. The chiral couplings to the fermions are asymptotically free, opening interesting perspectives for a possible solution to the gauge hierarchy problem. We argue that the interacting theory for such fields can be consistently quantized, in contrast to the free theory which is plagued by unstable solutions. We suggest that at the scale where the chiral couplings grow large the electroweak symmetry is spontaneously broken and a mass term for the chiral tensors is generated nonperturbatively. Massive chiral tensors correspond to massive spin-one particles that do not have problems of stability. We also propose an equivalent formulation in terms of gauge fields.

Quantum-classical interactions through the path integral

I consider the case of two interacting scalar fields, $\ensuremath{\phi}$ and $\ensuremath{\psi}$, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field which should be an improvement of the usual semiclassical procedure. As an application I use this method in order to enforce Gauss's law as a classical equation in a non-Abelian gauge theory. I argue that the theory is renormalizable and equivalent to the usual Yang-Mills theory as far as the gauge field terms are concerned. There are additional terms in the effective action that depend on the Lagrange multiplier field $\ensuremath{\lambda}$ that is used to enforce the constraint. These terms and their relation to the confining properties of the theory are discussed.

Einstein-Yang-Mills solutions in higher dimensional de Sitter spacetime

We consider particlelike and black hole solutions of the Einstein-Yang-Mills system with positive cosmological constant in d>4 spacetime dimensions. These configurations are spherically symmetric and present a cosmological horizon for a finite value of the radial coordinate, approaching asymptotically the de Sitter background. In the usual Yang-Mills case, we find that the mass of these solutions, evaluated outside the cosmological horizon at future/past infinity, generically diverges for d>4. Solutions with finite mass are found by adding to the action higher order gauge field terms belonging to the Yang-Mills hierarchy. A discussion of the main properties of these solutions and their differences from those of the usual Yang-Mills model, both in four and higher dimensions, is presented.

Higher-derivative gauge field terms in the M-theory action

We use superparticle vertex operator correlators in the light-cone gauge to determine the (DF)^2 R^2 and (DF)^4 terms in the M-theory effective action. Our results, when compactified on a circle, reproduce terms in the type-IIA string effective action obtained through string amplitude calculations.

Formula omitted]: sign of the times

We discuss the signature of space–time in the context of the E 11 -conjecture. In this setting, the space–time signature depends on the choice of basis for the “gravitational subalgebra” A 10 , and Weyl transformations connect interpretations with different signatures of space–time. Also the sign of the 4-form gauge field term in the Lagrangian enters as an adjustable sign in a generalized signature. Within E 11 , the combination of space–time signature ( 1 , 10 ) with conventional sign for the 4-form term, appropriate to M-theory, can be transformed to the signatures ( 2 , 9 ) and ( 5 , 6 ) of Hull's M * - and M ′ -theories (as well as ( 6 , 5 ) , ( 9 , 2 ) and ( 10 , 1 ) ) . Theories with other signatures organize in orbits disconnected from these theories. We argue that when taking E 11 seriously as a symmetry algebra, one cannot discard theories with multiple time-directions as unphysical. We also briefly explore links with the SL ( 32 , R ) conjecture.

THE MECHANISM OF MIGDAL RECURSION RELATION AND PHASE DIAGRAMS OF YANG–MILLS FIELDS

In this paper it is shown that the gauge fixing term is not only gauge fixing term in D dimensions, but also the mass term for gauge field in (D+2)-dimensional superspace [or (D-2)-dimensional space], more importantly the kinetic term for the gauge modes g(x) is the so-called (D-2)-dimensional SU (N)× SU (N) principal chiral model. The results conform Migdal's scheme about the connection between four-dimensional gauge field and two-dimensional chiral system. And the recursion relation can be generalized to D dimensions gauge theories with chiral models in D-2 dimensions. With the new local order parameter for Yang–Mills field <g>|D-2, the results are consistent with lattice results qualitatively: there is no phase transition in low dimensions (D≤4), while in higher dimensions first-order phase transition appears between strong coupling region and weak coupling region.

Gauge fields, geometric phases, and quantum adiabatic pumps.

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.

Electroweak symmetry breaking and fermion masses from extra dimensions

We study higher-dimensional non-supersymmetric orbifold models where the Higgs field is identified with some internal component of a gauge field. We address two important and related issues that constitute severe obstacles towards model building within this type of constructions: the possibilities of achieving satisfactory Yukawa couplings and Higgs potentials. We consider models where matter fermions are localized at the orbifold fixed-points and couple to additional heavy fermions in the bulk. When integrated out, the latter induce tree-level non-local Yukawa interactions and a quantum contribution to the Higgs potential that we explicitly evaluate and analyse. The general features of these highly constrained models are illustrated through a minimal but potentially realistic five-dimensional example. Finally, we discuss possible cures for the persisting difficulties in achieving acceptable top and Higgs masses. In particular, we consider in some detail the effects induced in these models by adding localized kinetic terms for gauge fields.

Opaque branes in warped backgrounds

We examine localized kinetic terms for gauge fields which can propagate into compact, warped extra dimensions. We show that these terms can have a relevant impact on the values of the Kaluza-Klein (KK) gauge field masses, wave functions, and couplings to brane and bulk matter. The resulting phenomenological implications are discussed. In particular, we show that the presence of opaque branes, with non-vanishing brane-localized gauge kinetic terms, allow much lower values of the lightest KK mode than in the case of transparent branes. Moreover, we show that if the large discrepancies among the different determinations of the weak mixing angle would be solved in favor of the value obtained from the lepton asymmetries, bulk electroweak gauge fields in warped-extra dimensions may lead to an improvement of the agreement of the fit to the electroweak precision data for a Higgs mass of the order of the weak scale and a mass of the first gauge boson KK excitation most likely within reach of the LHC.

MASSIVE YANG–MILLS THEORY IN ABELIAN GAUGES

We prove the perturbative renormalizability of pure SU(2) Yang–Mills theory in the Abelian gauge supplemented with mass terms. Whereas mass terms for the gauge fields charged under the diagonal U(1) allow us to preserve the standard form of the Slavnov–Taylor identities (but with modified BRST variations), mass terms for the diagonal gauge fields require the study of modified Slavnov–Taylor identities. We comment on the renormalization group equations, which describe the variation of the effective action with the different masses. Finite renormalized masses for the charged gauge fields, in the limit of vanishing bare mass terms, are possible provided a certain combination of wave function renormalization constants vanishes sufficiently rapidly in the infrared limit.

Conformal field theory dual of the RS model with gauge fields in the bulk

It has been conjectured that the (weakly coupled) Randall-Sundrum (RS) model with gauge fields in the bulk is dual to a (strongly coupled) 4D conformal field theory (CFT) with an UV cut-off and in which global symmetries of the CFT are gauged. We elucidate features of this dual CFT which are crucial for a complete understanding of the proposed duality. We argue that the limit of no (or small) brane-localized kinetic term for bulk gauge field on the RS side (often studied in the literature) is dual to no bare kinetic term for the gauge field which is coupled to the CFT global current. In this limit, the kinetic term for this gauge field in the dual CFT is ``induced'' by CFT loops. Then, this CFT loop contribution to the gauge field 1PI two-point function is dual (on the RS side) to the full gauge propagator (i.e., including the contribution of Kaluza-Klein and zero-modes) with both external points on the Planck brane. We also emphasize that loop corrections to the gauge coupling on the RS side are dual to sub-leading effects in a large-N expansion on the CFT side; these sub-leading corrections to the gauge coupling in the dual CFT are (in general) sensitive to the strong dynamics of the CFT.

Duality in gravity and higher spin gauge fields

Dual field theory realisations are given for linearised gravity in terms of gauge fields in exotic representations of the Lorentz group. The field equations and dual representations are discussed for a wide class of higher spin gauge fields. For non-linear Einstein gravity, such transformations can be implemented locally in light-cone gauge, or partially implemented in the presence of a Killing vector. Sources and the relation to Kaluza-Klein monopoles are discussed.

Non-commutative world-volume interactions on D-brane and Dirac–Born–Infeld action

By integrating the Seiberg-Witten differential equation in a special path, we write ordinary gauge fields in terms of their non-commutative counterparts up to three non-commutative gauge fields. We then use this change of variables to write ordinary abelian Dirac-Born-Infeld action in terms of non-commutative fields. The resulting action is then compared with various low energy contact terms of world-sheet perturbative string scattering amplitudes from non-commutative D$p$-brane. We find completely agreement between the field theory and string theory results. Hence, it shows that perturbative string theory knows the solution of the Seiberg-Witten differential equation.

Topological entanglement of polymers and Chern-Simons field theory

In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static polymers or in a lattice of obstacles is considered. The extension to the case in which the configurations of two or more polymers become non-static is not straightforward unless their trajectories are severely constrained. In this paper we present another approach, based on Chern--Simons field theory, which is able to describe the topological entanglements of two fluctuating polymers in terms of gauge fields and second quantized replica fields.

Superspace geometry for supermembrane backgrounds

We construct part of the superspace vielbein and tensor gauge field in terms of the component fields of 11-dimensional on-shell supergravity. The result can be utilized to describe supermembranes and corresponding matrix models for Dirichlet particles in non-trivial supergravity backgrounds to second order in anticommuting coordinates. We exhibit the κ-invariance of the corresponding supermembrane action, which at this order holds for unrestricted supergravity backgrounds, the supersymmetry covariance and the corresponding surface terms in the action.

Stokes Theorem for Loop Variables of Non-Abelian Gauge Field

A simple analytic proof of the formula known as the non-Abelian Stokes theorem is given. It is explicitly shown that the consistency of the formula is guaranteed by the Bianchi identity for the gauge field. An attempt is made to construct the Lagrangian for the gauge field in terms of loop variables.

Different approaches for bosonization in higher dimensions

We describe two distinct approaches for bosonization in higher dimensions; one is based on a direct comparison of current correlation functions while the other relies on a master Lagrangian formalism. These are used to bosonize the massive Thirring model in three and four dimensions in the weak coupling regime but with an arbitrary fermion mass. In both approaches the explicit bosonized Lagrangian and current are derived in terms of gauge fields. The complete equivalence of the two bosonization methods is established. Exact results for the free massive fermion theory are also obtained. Finally, the two-dimensional theory is revisited and the possibility of extending this analysis for arbitrary dimensions is indicated.

Gauge field theory for functional graded materials and components

A direct approach for the solution of problems in condensed matter, and particularly in functional graded materials (FGMs) is presented in terms of gauge fields. The heat flow in an FGM is considered as an example, although the approach is applicable to any field in a material (mechanical, magnetic, electric, gravitational, etc.) of any complex structure with arbitrary defects (e.g. grain boundaries, dislocations, impurities). The approach suggested could be applied also to FGM components of different shape instead of the currently employed FEM approximations of exact solutions.