An energy-momentum tensor in gauge theories

We consider the renormalization of the twist two, dimension four gauge invariant operator O_μν⁽¹⁾ = − F_μσF_νσ − g_{μν 0}. By using the general theory of renormalization of gauge invariant operators, we find the gauge noninvariant operator O⁽²⁾ with which it mixes. We construct a finite combination of O⁽¹⁾ and O⁽²⁾ and show that it is an acceptable energy momentum tensor for gauge theories. We compare our energy momentum tensor with that constructed by Freedman, Muzinich, and Weinberg.     

The β function,scaling, and improved action forSU(3) lattice gauge theory

We present a detailed analysis of the nonperturbativeβ function along the Wilson axis for theSU(3) pure gauge theory using the Monte Carlo renormalization group method. The scaling behavior of the string tension, the deconfinement transition temperature, and the O⁺⁺ glueball mass obtained from published data is compared. The results show that there is no asymptotic scaling forK _F=(6/g ²)<6.1. We also estimate the renormalized action generated by the √3 block transformation for use in future calculations.     

Unparticles in gauge theory

A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle (“ungluon”). The model is formulated in terms of Lagrangian which features the source field S(x) which becomes a local pseudo-Goldstone field of conformal symmetry — the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by B _μ(x) ∼ ∂_μ S(x). Because the conformal sector is strongly coupled, the mode S(x) may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the “ungluon” exchange pattern — the “ungluon” propagator.     

The Gribov–Zwanziger action in the presence of the gauge invariant,nonlocal mass operator Tr∫d<Superscript>4</Superscript>xF<Subscript>μν</Subscript>(D<Superscript>2</Superscript>)<Superscript>-1</Superscript>F<Subscript>μν</Subscript> in the Landau gauge

We prove that the nonlocal gauge invariant mass dimension 2 operator F_μν(D²)^-1F_μν can be consistently added to the Gribov–Zwanziger action, which implements the restriction of the path integral’s domain of integration to the first Gribov region when the Landau gauge is considered. We identify a local polynomial action and prove the renormalizability to all orders of perturbation theory by employing the algebraic renormalization formalism. Furthermore, we also pay attention to the breaking of the BRST invariance, and to the consequences that this has for the Slavnov–Taylor identity. PACS 11.15.-q; 11.15.Tk     

General theory of renormalization of gauge theories in nonlinear gauges

We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.     

Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to the BRST formalism. The above four (3+1)-dimensional (4D) theory is considered on a (4, 2)-dimensional supermanifold parameterized by the four even spacetime variables x ^μ (with μ=0,1,2,3) and a pair of odd Grassmannian variables θ and (with ). One of the salient features of our present investigation is that the above nilpotent (anti-) BRST symmetry transformations turn out to be absolutely anticommuting due to the presence of a Curci–Ferrari (CF) type of restriction. The latter condition emerges due to the application of our present superfield formalism. The actual CF condition, as is well known, is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that our present 4D Abelian 2-form gauge theory imbibes some of the key signatures of the 4D non-Abelian 1-form gauge theory. We briefly comment on the generalization of our superfield approach to the case of Abelian 3-form gauge theory in four, (3+1), dimensions of spacetime.     

Neutral currents in left-right symmetric gauge models

We analyse all the neutral-current phenomena following from the general class of gauge models based on the group SU(2) _L ⊗ SU(2) _R ⊗ U(1). It is found that the neutral-current couplings in these models bear a remarkable similarity to those in the standard Weinberg-Salam gauge model. The parameter which plays the role of sin²ϑ_w is found to lie between 0 and 1/2. Comparison with experimental data shows that even a model with the ratio of the masses of the twoZ bosons as small as 1.9 is not ruled out.     

A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator

This paper presents a complete algebraic proof of the renormalizability of the gauge invariant d=4 operator F _{μ ν} ²(x) to all orders of perturbation theory in pure Yang–Mills gauge theory, whereby working in the Landau gauge. This renormalization is far from being trivial as mixing occurs with other d=4 gauge variant operators, which we identify explicitly. We determine the mixing matrix Z to all orders in perturbation theory by using only algebraic arguments and consequently we can uncover a renormalization group invariant by using the anomalous dimension matrix Γ derived from Z. We also present a future plan for calculating the mass of the lightest scalar glueball with the help of the framework we have set up.     

SU2 ⊗ U1 gauge model of electroweak interaction with (V + A) strangeness-changing charged current

We construct a model of renormalizable electroweak interaction with (V+A) strangeness-changing charged current in the framework of the minimal spontaneously broken SU₂ ⊗ U₁ gauge theory, taking our motivation from the recently reported measurement of the electron asymmetry in polarizedΣ ⁻-hyperonβ-decay by Keller and co-workers. The model avoids strangeness-changing but admits charm-changing pieces in the neutral current. Several phenomenological consequences of the model are discussed together with a comparison with the standard model of electroweak interaction.     

Composite model of gauge bosons in electroweak interactions

We consider a simple Lagrangian which is constructed by only the preon and antipreon fields. By introducing the auxiliary fields φ_μ, φ _μ ^† , and ϕ_μ, it is shown that φ_μ, φ _μ ^† , and ϕ_μ correspond to the electroweak gauge bosonsW _μ ⁺ ,W _μ ⁻ , andW _μ ³ , respectively, which are composite particles of preons and antipreons.     

Extra neutral gauge boson from two versions of the 3-3-1 model in future linear colliders

Our aim is to establish some signatures of the extra gauge boson Z^′, predicted in two versions of the SU(3)_C×SU(3)_L×U(1)_X model and to show possible differences between these signatures. First, by considering the process e⁺+e^-→μ⁺+μ^-, we obtain some observables and next, by considering additional hadronic final states, we obtain lower bounds for M_Z′, within 95% C.L. We also include our preliminary results concerning pp̄ and pp collisions in order to support our conclusions about the possibility to discriminate different versions of the 3-3-1 model. From our analysis we conclude that linear colliders can show a clear signature for the existence of Z^′ predicted in the 3-3-1 model and also that it can discriminate the various versions. PACS 12.60.Cn; 13.66.De; 13.66.Fg; 14.70.Pw     

Convergence and gauge dependence properties of the resummed one-loop quark-quark scattering amplitude in perturbative QCD

The one-loop QCD effective charge α _s ^eff for quark-quark scattering is derived by diagrammatic resummation of the one-loop amplitude using an arbitrary covariant gauge. Except for the particular choice of gauge parameter ξ = −3, α _s ^eff is found to increase with increasing physical scale, Q, as lnQ or ln² Q. For ξ = −3, α _s ^eff decreases with increasing Q and satisfies a renormalization group equation. Also, except for the case ξ = 19/9, convergence radii of geometric series are found to impose upper limits on Q. The text was submitted by the author in English.     

Non-linear Stability of Modulated Fronts¶for the Swift–Hohenberg Equation

We consider front solutions of the Swift–Hohenberg equation ∂ _t u= -(1+ ∂ _x ²)² u + ɛ² u -u ³. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using renormalization techniques and a decomposition into Bloch waves, we show the non-linear stability of these solutions. It turns out that this problem is closely related to the question of stability of the trivial solution for the model problem ∂ _t u(x,t) = ∂ _x ² u (x,t)+(1+tanh(x-ct))u(x,t)+u(x,t) ^p with p>3. In particular, we show that the instability of the perturbation ahead of the front is entirely compensated by a diffusive stabilization which sets in once the perturbation has hit the bulk behind the front. Received: 23 February 2001 / Accepted: 27 August 2001     

Noncommutative electromagnetism as a large <Emphasis Type="Italic">N</Emphasis> gauge theory

We map noncommutative (NC) U(1) gauge theory on ℝ _C ^d ×ℝ _NC ²ⁿ to U(N→∞) Yang–Mills theory on ℝ _C ^d , where ℝ _C ^d is a d-dimensional commutative spacetime while ℝ _NC ²ⁿ is a 2n-dimensional NC space. The resulting U(N) Yang–Mills theory on ℝ _C ^d is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang–Mills theory onto ℝ _C ^d . We show that the gauge-Higgs system (A _μ ,Φ ^a ) in the U(N→∞) Yang–Mills theory on ℝ _C ^d leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4{\mathcal{N}}=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A _μ ,Φ ^a ) in half-BPS configurations describes self-dual Einstein gravity.     

Potentials of pointlike particles in gauge theory with a dilaton

I examine the potential of a pointlike particle carrying SU (N _c) charge in a gauge theory with a dilaton. The potential depends on boundary conditions imposed on the dilaton: For a dilaton that vanishes at infinity the resulting potential is a regulatized Coulomb potential of the form (r+r _ϕ)⁻¹, withr _ϕ, inversely proportional to the decay constant of the dilaton. Another natural constraint on the dialaton ϕ is independence of (1/g ²) exp(ϕ/f_ϕ) from the gauge couplingg. This requirement yields a confining potential proportional tor.     

On the excited state wave functions of Dirac fermions in the random gauge potential

In the last decade, it was shown that the Liouville field theory is an effective theory of Dirac fermions in the random gauge potential (FRGP). We show that the Dirac wave functions in FRGP can be written in terms of descendents of the Liouville vertex operator. In the quasiclassical approximation of the Liouville theory, our model predicts that the localization length ξ scales with the energy E as $ \xi \sim E^{{{ - b^2 } \mathord{\left/ {\vphantom {{ - b^2 } {(1 + b^2 )^2 }}} \right. \kern-\nulldelimiterspace} {(1 + b^2 )^2 }}} $ \xi \sim E^{{{ - b^2 } \mathord{\left/ {\vphantom {{ - b^2 } {(1 + b^2 )^2 }}} \right. \kern-\nulldelimiterspace} {(1 + b^2 )^2 }}} , where b is the strength of the disorder. The self-duality of the theory under the transformation b → 1/b is discussed. We also calculate the distribution functions of t ₀ =|ψ ₀(x)|², (i.e. p(t ₀); ψ ₀(x) is the ground state wave function), which behaves as the log-normal distribution function. It is also shown that in small t ₀, p(t ₀) behaves as a chi-square distribution.     

Colour effects in Drell-Yan process

We examine the predictions of gauge theories with colour excitation for the processpp →μ ⁺ μ ⁻ X. Relative to the predictions of quark parton model (with three colours) we find enhancements as large as a factor 3 – 4 for the cross-sectionM ³ d ² σ/dMdy|_y=0 in the region 0·03 ≲M/√s ≲ 0·2 at √s=62 GeV,M being the invariant mass andy the rapidity of the muon pair. We study the sensitivity of this result to the colour gluon mass and the underlying parametrisation of the quark and gluon distribution functions.     

Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian

We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.     

Confinement and mass gap in abelian gauge

First, we present a simple confining abelian pure gauge theory. Classically, its kinetic term is not positive definite, and it contains a simple UV regularized F⁴ interaction. This provokes the formation of a condensate such that, at the saddle point of the effective potential, the wave function normalization constant of the abelian gauge fields vanishes exactly. Then we study SU(2) pure Yang-Mills theory in an abelian gauge and introduce an auxiliary field for a BRST invariant condensate of dimension 2, which renders the charged sector massive. Under simple assumptions its effective low energy theory reduces to the confining abelian model discussed before, and the VEV of is seen to scale correctly with the renormalization point. Under these assumptions, the confinement condition Z _eff = 0 also holds for the massive charged sector, which suppresses the couplings of the charged fields to the abelian gauge bosons in the infrared regime. Received: 27 November 2002 / Published online: 14 April 2003 RID="a" ID="a" e-mail: Ulrich.Ellwanger@th.u-psud.fr RID="b" ID="b" e-mail: Nicolas.Wschebor@th.u-psud.fr ^* Unité Mixte de Recherche - CNRS - UMR 8627     

The one-loop Green’s functions of dimensionally reduced gauge theories

We apply the dimensional regularization technique as well as that by dimensional reduction to the calculation of the regularized one-loop Green’s functions ind ₀-dimensional Yang-Mills theory with real massless scalars and spinors in arbitrary (real) representations of a gauge groupG. As a particular example, the super-symmetrically regularized one-loop Green’s functions of theN=4 supersymmetric Yang-Mills model are derived.