16408269
Monopoles, noncommutative gauge theories in the BPS limit and some simple gauge groups
For three conspicuous gauge groups, namely, SU(2), SU(3) and SO(5), and at first order in the noncommutative parameter matrix hθμν, we construct smooth monopole — and, some two-monopole — fields that solve the noncommutative Yang-Mills-Higgs equations in the BPS limit and that are formal power series in hθμν. We show that there exist noncommutative BPS (multi-)monopole field configurations that are formal power series in hθμν if, and only if, two a priori free parameters of the Seiberg-Witten map take very specific values. These parameters, that are not associated to field redefinitions nor to gauge transformations, have thus values that give rise to sharp physical effects.
121374470
Fermionic langevin equations without kernel and Zwanzinger's gauge fixing procedure☆
Abstract We study the compatibility of Zwanzinger's gauge fixing procedure and the Langevin equations without kernel for massive fermions from the renormalization theory point of view. The UV divergent part of the QED fermionic propagator is computed at the one-loop level. The problems encountered in its subtraction are analyzed.
117863195
Chiral gauge anomalies on noncommutative space-time
The consistent form and the covariant form of the gauge anomaly for fundamental U(N) chiral fermions on even-dimensional noncommutative space-time are computed and discussed.
118419260
SO(10) GUTs with large tensor representations on Noncommutative Space-time
We construct a noncommutative version of a general renormalizable SO(10) GUT with Higgses in the 210, $\overline{126}, 45, 10$ and 120 irreps of SO(10) and a Peccei-Quinn symmetry. Thus, we formulate the noncommutative counterpart of a non-supersymmetric SO(10) GUT which has recently been shown to be consistent with all the physics below $M_{GUT}$. The simplicity of our construction --the simplicity of the Yukawa terms, in particular-- stems from the fact that the Higgses of our GUT can be viewed as elements of the Clifford algebra $\mathbb{C}\rm{l}_{10}(\mathbb{C})$; elements on which the SO(10) gauge transformations act by conjugation. The noncommutative GUT we build contains tree-level interactions among different Higgs species that are absent in their ordinary counterpart as they are forbidden by SO(10) and Lorentz invariance. The existence of these interactions helps to clearly distinguish noncommutative Minkowski space-time from ordinary Minkowski space-time.
17379629
The noncommutative U(1) Higgs-Kibble model in the enveloping-algebra formalism and its renormalizability
We discuss the renormalizability of the noncommutative U(1) Higgs-Kibble model formulated within the enveloping-algebra approach. We consider both the phase of the model with unbroken gauge symmetry and the phase with spontaneously broken gauge symmetry. We show that against all odds the gauge sector of the model is always one-loop renormalizable at first order in θμν, perhaps, hinting at the existence of a new symmetry of the gauge sector of the model. However, we also show that the matter sector of the model is non-renormalizable whatever the phase.
122147161
The light-cone gauge, Chern-Simons theory and topologically massive Yang-Mills theory
Abstract In this paper, we complete our study of one-loop perturbative Chern-Simons theory in the light-cone gauge n · A a = 0, n 2 = 0. Using a gauge-invariant regularization procedure, which defines Chern-Simons theory as the large-mass limit of a topologically massive field theory, we evaluate the three-point function Λ μνω abc ( p 1 , p 2 , p 3 ) to one loop. The spurious poles of ( q · n ) −1 in the gauge propagator are treated with the n μ ∗ - prescription . It is shown that the vertex function, which contains both local and nonlocal terms, is UV finite, respects the Ward identity and agrees with the one-loop effective action proposed in the preceding paper.
120098848
THE DEPENDENCE OF THE TEMPORAL GAUGE GREEN FUNCTIONS ON THE GAUGE-FIXING VECTORS THROUGH BRS SYMMETRY
The UV-divergent part of the one-loop contribution to the vacuum polarization tensor is shown to satisfy the BRS identities governing its dependence on the time-like vector n and the auxiliary space-like vector n′ introduced by the generalized Leibbrandt-Mandelstam (LM) prescription. As far as we know the BRS identity for the n′ dependence cannot be obtained within the pragmatic approach to the LM prescription. In order to circumvent the problem the LM prescription is incorporated into a BRS-invariant action. The BRS identity for n′ provides an example of a situation where terms of order η combine with loop integrals that are singular as η→0 yielding a finite contribution.
16683941
Ground state properties and glueball spectrum in SU(2) Yang-Mills theory using gauge invariant variables
We describe a nonperturbative calculation of the spectrum of SU(2) Yang-Mills theory based on a Hamiltonian formulation. Our approach exploits gauge invariant variables similar to those used in nuclear physics to describe collective motion in nuclei.
118578498
Remarks on the Renormalisation of Fermions Coupled to Gauge Fields in the Zwanziger Gauge
The renormalisation of fermions coupled to gauge fields in the Stochastic Quantisation formalism is not a trivial subject. In order to simplify the discussion we shall consider QED in the Zwanziger gauge. It shall become clear that the conclusions we will get applies to the non-abelian case as well.
120228894
Perturbative Chern-Simons theory in the light cone gauge: The One loop vacuum polarization tensor in a gauge invariant formalism
Abstract Perturbative Chern-Simons (CS) theory, with gauge group SU( N ), is studied in the physical light-cone gauge n σ A σ a = 0, n 2 = 0. Using a gauge-invariant regularization procedure, we compute the vacuum polarization tensor to one-loop order. The regularized theory is consistent with BRS invariance. It is shown that the vacuum polarization tensor is UV finite and transverse, but contains one non-local term which is strictly gauge-dependent. A finite, non-multiplicative (gauge-dependent) wave function renormalization enables us to express the one-loop effective action as Γ one-loop ( A μ (ren) , k ) = (( k + sign( k ) c v )/4 π ) S CS ( A μ (ren) , where S CS is the classical action and k is the bare Chern-Simons parameter.
120311682
The three-gluon vertex in the temporal-planar gauge with the Leibbrandt-Vienna prescription: The one-loop effective action
Abstract The UV-divergent part of the one-loop contribution to the three-gluon vertex, Γμνϱabc, is computed in the temporal-planar gauge. The generalized Leibbrandt-Mandelstam (or Leibbrandt-Vienna) prescription - which is free from the inconsistencies that are known to affect the principal value prescription - is used to define the unphysical poles 1/(k·n)j. We compute the (one-loop) UV-divergent part of the gauge-field effective action up to order g3. We show that all the awkward non-local divergences can be written as the BRS variation of some functional X whereas the β-function coincides with the usual (covariant) result. In the homogeneous case we show that a non-local renormalization of the gauge field Aμa of the form A 0μ a = Z g − 1 2 A μ a − h ƒ μ a (A), A 0μ a and A μ a having identical gauge transformations, and the usual coupling constant renormalization, g0 = Zgμ2ϵg, suffice to get rid of all the UV-divergences in Γμνϱabc and the vacuum polarization tensor gPμνab.