On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

Gluon-ghost condensate of mass dimension 2 in the Curci-Ferrari gauge

The effective potential for an on-shell BRST invariant gluon-ghost condensate of mass dimension 2 in the Curci-Ferrari gauge in SU(N) Yang-Mills is analysed by combining the local composite operator technique with the algebraic renormalization. We pay attention to the gauge parameter independence of the vacuum energy obtained in the considered framework and discuss the Landau gauge as an interesting special case.     

General covariance of the non-abelian DBI-action: checks and balances

We perform three tests on our proposal to implement diffeomorphism invariance in the non-abelian D0-brane DBI action as a base-point independence constraint between matrix Riemann normal coordinate systems. First, we show that T-duality along an isometry correctly interchanges the potential and kinetic terms in the action. Second, we show that the method to impose base-point independence using an auxiliary dN²-dimensional nonlinear sigma model also works for metrics which are curved along the brane, provided a physical gauge choice is made at the end. Third, we show that without alteration this method is applicable to higher order in velocities. Testing specifically to order 4, we elucidate the range of validity of the symmetrized trace approximation to the non-abelian DBI action.     

Remark on the consistent gauge anomaly in supersymmetric theories

We present a direct field theoretical calculation of the consistent gauge anomaly in the superfield formalism, on the basis of a definition of the effective action through the covariant gauge current. The scheme is conceptually and technically simple and the gauge covariance in intermediate steps reduces calculational labors considerably. The resultant superfield anomaly, being proportional to the anomaly d^abc=trT^a{T^b,T^c}, is minimal without supplementing any counterterms. Our anomaly coincides with the anomaly obtained by Marinković as the solution of the Wess–Zumino consistency condition.     

Spontaneous symmetry breaking in massless field theories,finite temperature and criticality

We study the behaviour at finite temperature of massless field theories exhibiting spontaneously broken solutions. We establish the occurence of a phase transition of the first kind at some critical point T_c which can be calculated to any finite order in perturbation theory. Similarly, perturbative methods can be used for thermodynamic functions in all regions, including the critical region. For the case of a gauge theory, we demonstrate the gauge independence of the critical point, the thermodynamic potentials and the order parameter to all orders of perturbation theory.     

QCD cascade model in deep inelastic scattering

We develop a new QCD cascade model for jets in deep inelastic scattering. We use the light-like axial gauge whose gauge vector is parallel to momentum of the initial parton so that only final partons cascade. Due to this feature we can generate events for any given virtualityQ ² andx _B =Q ²/2Pq.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

Infrared properties of two-loop,initial state spectator interactions in the Drell-Yan process

We use the light-cone axial gauge of proper-time ordered perturbation theory and study the soft-IR properties of the two-loop virtuals' diagrams considered by Bodwin, Brodsky and Lepage for ππ → μ⁺μ^- + X. It is shown that although the systematic summation over all possible spectator interactions removes the outside soft-IR divergences in the non-overlapping ladder Glauber diagrams, unphysical inside soft-IR divergences persist. So, in the light-cone axial gauge the on-shell Glauber region is not a gauge invariant concept which can be physically isolated from radiative corrections which non-trivially involve other diagrammatic regions. Due to gauge invariance it can be potentially misleading in eikonal phenomenologies based on perturbative QCD to assume an ad hoc inside soft-IR cutoff in analyzing possible non-abelian effects in multiple scatterings involving spectators.     

Corrections to the Zτ +τ− vertex in topcolor-assisted technicolor theory

We calculate the corrections to the Zτ⁺τ^? vertex in the one-family topcolor-assisted technicolor models without exact custodial symmetry contributed from the exchange of extended technicolor (ETC) sideways and diagonal gauge bosons and the topcolor gauge boson Z′. The precise measurements of the τ asymmetry parameter Aτ give strong constraint on the free parameters in the topcolor-assisted technicolor models.     

Gauge coupling renormalisation with several U(1) factors

We examine the renormalisation of gauge coupling constants in theories with a G × U(1)^N gauge group (which appears to be the gauge symmetry of many possible superstring vacua). In general, the abelian gauge bosons mix among themselves, so a correct renormalisation requires including this mixing in the evolution of the gauge couplings. We present general results and note that the mixing is scale independent to all orders if the renormalization group trajectory passes through a unification point. We discuss the cases of one loop and two loops explicitly. An example, based on a possible superstring-inspired model, is given.     

A non-perturbative calculation of the infrared limit of the axial gauge gluon propagator (I)

We describe a non-perturbative study of the infrared behavior of the axial gauge gluon propagator based on the Dyson equation and Ward identities. We conclude that the propagator Δ_μν(q) displays a q^?4 singularity in the infrared limit, and that consequently the axial gauge running coupling constant g_A²)(q) displays a q^?2 singularity in the same limit. The only assumption necessary to obtain this conclusion is that the transverse part of the triple-gluon vertex function does not dominate the longitudinal part in the infrared regime.     

Gauge independence of the effective potential revisited

We apply the formalism of extended BRS symmetry to the investigation of the gauge dependence of the effective potential in a spontaneously symmetry broken gauge theory. This formalism, which includes a set of Grassmann parameters defined as the BRS variations of the gauge-fixing parameters, allows us to derive in a quick and unambiguous way the related Nielsen identities, which express the physical gauge independence, in a class of generalized 't Hooft gauges, of the effective potential. We show in particular that the validity of the Nielsen identities does not require any constraint on the gauge-fixing parameters, contrary to some claims found in the literature. We use the method of algebraic renormalization, which leads to results independent of the particular renormalization scheme used.     

Possible structures of the neutral current within a gauge theory framework

We examine a class of gauge theories based on U(1)×SU(2)×G allowing for an arbitrary number of gauge bosons, while retaining the lowq ² four fermion interaction of the standard model. Measurable consequences fore ⁺ e ^?→μ ⁺ μ ^? ande ⁺ e ^?→e ⁺ e ^? at presently available as well as LEP energies are presented. Implications of the recently determined QED cut-offΛ _? ? 100 GeV on gauge boson properties and the anomalous magnetic moment of the muon are pointed out.     

On the vacuum structure of an SU(2) Yang-Mills theory

By using a compactification of the spatial part R³ of Minkowski-space different from the one-point compactification to S³, we get a new classification of the vacua for an SU(2) gauge theory. It contains, besides the vacua arising in the S³ compactification, the Gribov vacua as new classes. We discuss the role of pseudoparticle solutions within this framework and comment on the problem of the Coulomb gauge degeneracy.     

Type IIB Green-Schwarz superstrings in AdS 5 × S 5 from the supercoset approach

We consider superstrings moving in the AdS ₅ × S ⁵ space-time and find their Green-Schwarz action using the supercoset approach based on the supergroup PSU(2, 2|4). We describe several parametrizations of the relevant supercoset and present the action in different κ-symmetry gauges. In particular, we discuss a gauge where all the fermionic coordinates corresponding to the conformal (S) supercharges are gauged away and also a light-cone type gauge where half of the Q and S supercoordinates are gauged away. The resulting action contains terms that are quadratic and quartic in fermions. In the flat-space limit, it reduces to the standard light-cone Green-Schwarz action. We comment on the possibility of fixing the bosonic light-cone gauge and of reformulating the action in terms of two-dimensional Dirac spinors.     

Yang-Mills theories in space-like axial and planar gauges

The quantization of Yang-Mills theories according to a canonical procedure is studied first in the axial gauge A₃^a ≡ 0. We show that the perturbative S-matrix cannot be expressed in terms of well-defined distributions in a Hilbert space involving only physical states without conflicting with unitarity. We then resort to the space-like planar gauge and show that it is possible to define a perturbative S-matrix at the price of introducing a set of free ghost fields. The S-matrix is unitary in the subspace of the physically acceptable states on which A₃^a vanish.     

A compensating functional method in the massive Yang-Mills theory

In the massive and massless Yang-Mills theories the generating functional (the S-matrix) independence of the gauge parameter is provided on the mass shell without introducing an extra degree of freedom (gauge group integration).