The generalized radiation gauge for a simply connected space-time

In the following we shall make some remarks on the existence of the generalized radiation gauge if space-timeM is topologically non trivial (M R ⁴). This specialU(1)-gauge generalizes in a sense the wellknown Coulomb gauge and if it is possible to use that gauge the Maxwell equations reduce to a well defined elliptical eigenvalue problem. This can be discussed using, for example, the Hodge theory and the theory of the spectrum of elliptic differential operators.     

The calculation of the hadron spectrum in lattice QCD with dynamical quarks

Hadron masses are calculated on an 8³×16 lattice using four flavors of staggered fermions to generate the gauge configurations, but using Wilson fermions to calculate the hadron propagators. The identification of a value of the Wilson hopping parameter with the value of the bare quark mass used in the simulations is discussed.     

The inaction approach to gauge theories

The inaction approach introduced previously for φ⁴ [1] is generalized to gauge theories. It combines the advantages of the effective field theory and causal approaches to quantum fields. Also, it suggests ways to generalizing gauge theories.     

Induced gauge theory on a noncommutative space

We consider a scalar φ⁴ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action, using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model. PACS 11.10.Nx; 11.15.-q     

The renormalization flow in the adjoint SU(2) lattice Higgs model

Applying the Monte Carlo renormalization group method we investigate the flow of coupling constants for the 8⁴ and 16⁴ SU(2) lattice Higgs model with triplet Higgs fields. The couplings of the renormalized actions are determined using Schwinger-Dyson equations. From the flow we find new evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β but no indication for a discontinuity fixed point.     

A nonperturbative variational approach to the vacuum structure in quantum chromodynamics

We study the vacuum structure in QCD in a nonperturbative manner using a variational approach with gluon condensates. We show that in Coulomb gauge as the coupling becomes moderately strong, the perturbative vacuum of QCD becomes unstable leading to gluon condensates and a gauge dependent effective mass for the gluons related to the gauge independent value of 〈vac‖G _μν ^a G ^aμν‖vac〉 of Shifmanet al.     

The Parametrization Invariant and Gauge Invariant Effective Actions in Quantum Field Theory

The review of formulation and methods of calculation of the parametrization and gauge invariant effective actions in quantum field theory is given. As an example the Vilkovisky-De Witt Effective action (EA) is studied (this EA is a natural representative of gauge and parametrization invariant EA's). The examples where the use of the standard EA leads to the ambiguity are demonstrated. This happens as the result of dependence of the standard EA upon the choice of gauge condition. These examples are as follows: Coleman-Weinberg potential in the finite theories and symmetry breaking, EA in quantum gravity with matter and d = 5 gauged supergravity, the possibility of spontaneous supersymmetry breaking in N = 1 supergravity and the spontaneous compactification in the multidimensional R²-gravity. In all these cases the one-loop Vilkovisky-De Witt EA is found and therefore the problem of gauge dependence of EA is solved. The dependence of standard EA of composite fields upon the gauge is studied for the general gauge theories. The class of gauge and parametrization invariant EA's of the composite fields is offered.     

The polarization-asymmetry correlation of107In and parity violation

We report on the first measurements of the longitudinal polarization of positrons emitted by polarized nuclei, using cryogenically polarized¹⁰⁷In. This so-called polarization-asymmetry correlation is very sensitive to the mass of a possible right-handed gauge boson, which is invoked by parity symmetric extensions of the standard V-A electroweak model to explain the experimentally observed strong violation of parity which, however, may not be complete. The positron polarization is deduced from the time-resolved decay spectrum of positronium hyperfine states. Our preliminary result points to a lower limit of about 210 GeV for the mass of an eventual right-handed charged W gauge boson. This result can still be improved.     

Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2⁺ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2⁺ and 2⁻ particles of equal mass, as well as a massive pseudoscalar.     

Lorentz invariant exact solution of the anomalous chiral Schwinger model

We present an exact solution of the anomalous chiral Schwinger model using Fermionic variables. We implement infrared regularization by considering the model on a spatial circleS ¹. Quantum effects modify the gauge constraints through the appearance of Schwinger terms in the gauge algebra. We perform a careful analysis of the resulting second class gauge constraints by implementing Dirac's method at the quantum level and obtain the spectrum of the theory. We get a consistent unitary Lorentz invariant theory for particular values of the counterterms. We find that when we regulate the fermionic sector of the model without reference to the gauge fields Lorentz invariance requires that we add both Lorentz variant and gauge variant counterterms.     

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.     

The conformal anomaly and the neutral currents sector of the Standard Model

We elaborate on the structure of the graviton–gauge–gauge vertex in the electroweak theory, obtained by the insertion of the complete energy–momentum tensor (T  ) on 2-point functions of neutral gauge currents (VV^′$V{V}^{\prime }$). The vertex defines the leading contribution to the effective action which accounts for the conformal anomaly and related interaction between the Standard Model and gravity. The energy–momentum tensor is derived from the curved spacetime Lagrangian in the linearized gravitational limit, and with the inclusion of the term of improvement of a conformally coupled Higgs sector. As in the previous cases of QED and QCD, we find that the conformal anomaly induces an effective massless scalar interaction between gravity and the neutral currents in each gauge invariant component of the vertex. This is described by the exchange of an anomaly pole. We show that for a spontaneously broken theory the anomaly can be entirely attributed to the poles only for a conformally coupled Higgs scalar. In the exchange of a graviton, the trace part of the corresponding interaction can be interpreted as due to an effective dilaton, using a local version of the effective action. We discuss the implications of the anomalous Ward identity for the TVV^′$TV{V}^{\prime }$ correlator for the structure of the gauge/gauge/effective dilaton vertex in the effective action. The analogy between these effective interactions and those related to the radion in theories with large extra dimensions is pointed out.     

Kähler metrics and gauge kinetic functions for intersecting D6‐branes on toroidal orbifolds – The complete perturbative story

We systematically derive the perturbatively exact holomorphic gauge kinetic function, the open string Kähler metrics and closed string Kähler potential on intersecting D6‐branes by matching open string one‐loop computations of gauge thresholds with field theoretical gauge couplings in 𝒩 = 1 supergravity. We consider all cases of bulk, fractional and rigid D6‐branes on T⁶/Ω ℛ and the orbifolds T⁶/(ℤ_N × Ω ℛ) and T⁶/(ℤ₂ × ℤ_2M × Ω ℛ) without and with discrete torsion, which differ in the number of bulk complex structures and in the bulk Kähler potential. Our analysis includes all supersymmetric configurations of vanishing and non‐vanishing angles among D6‐branes and O6‐planes, and all possible Wilson line and displacement moduli are taken into account. The shape of the Kähler moduli turns out to be orbifold independent but angle dependent, whereas the holomorphic gauge kinetic functions obtain three different kinds of one‐loop corrections: a Kähler moduli dependent one for some vanishing angle independently of the orbifold background, another one depending on complex structure moduli only for fractional and rigid D6‐branes, and finally a constant term from intersections with O6‐planes. These results are of essential importance for the construction of the related effective field theory of phenomenologically appealing D‐brane models. As first examples, we compute the complete perturbative gauge kinetic functions and Kähler metrics for some T⁶/ℤ₂ × ℤ₂ examples with rigid D‐branes of [1]. As a second class of examples, the Kähler metrics and gauge kinetic functions for the fractional QCD and leptonic D6‐brane stacks of the Standard Model on T⁶/ℤ₆^′T⁶/ℤ₆^′ from [2] are given.     

The Landau gauge gluon propagator in lattice QCD

A Monte Carlo calculation of the gluon propagator in the Landau gauge in SU(3) lattice gauge theory is described. The results of calculations at β = 5.6 (200 4³ × 8 lattices), β = 5.8 (400 4³ × 10 lattices and 100 6³ × 12 lattices), and β = 6.0 (100 4³ × 8 lattices) indicate that the gluon propagator resembles a massive particle propagator in which the mass grows with separation. At the largest distances accessible with these lattices, the mass is about 600 MeV.     

The Non-Perturbative Approach to the Infrared Problem in QCD at Finite Temperature

A non-perturbative approach is developed for investigation of the infrared problem in QCD at T ≠ 0 in the ghost-free axial gauge. The problem is solved by using a 3-dimensional theory within the exact Slavnov-Taylor identities and Schwinger-Dyson equations. The system of two non-linear integral equations for the structural functions of the gluon polarization tensor is obtained whose solution determines the infrared behavior of the temperature Green functions in the 4-dimensional QCD. The simplest solution of these equations which is the same as the first term of the perturbation expansion shows the presence of singularities in the gluon propagator at momenta p ∼ g²T, that cannot be eliminated by any choice of the gauge. The infrared instability of QCD at T ≠ 0 caused by these singularities is discussed.     

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.     

Star products from commutative string theory

A boundary-state computation is performed to obtain derivative corrections to the Chern-Simons coupling between a p-brane and the RR gauge potential C ^p −3. We work to quadratic order in the gauge field strength F, but all orders in derivatives. In a certain limit, which requires the presence of a constant B-field background, it is found that these corrections neatly sum up into the *₂ product of (commutative) gauge fields. The result is in agreement with a recent prediction using noncommutativity.     

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.