5508416
Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism
Abstract We consider noncommutative gauge theory defined by means of Seiberg–Witten maps for an arbitrary semisimple gauge group. We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters θ . We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group. We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg–Witten maps that are linear in the matter fields. Surprisingly, it turns out that the UV divergent parts of the matter contributions are proportional to the noncommutative Yang–Mills action where traces are taken over the representation of the matter fields; this result supports the need to include such traces in the classical action of the gauge sector of the noncommutative theory.
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.
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.
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.
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.
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.
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.
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.
116367467
The Shift of the Chern-Simons parameter beyond one loop
119536533
Axial gauge Chern-Simons theory in the Leibbrandt-Mandelstam prescription for a certain class of UV regulators
Abstract We show that the complete perturbative effective action of an SU ( N ) Chern-Simons theory in an homogenous axial-type gauge ( nA a =0, n 2 >0, n 2 n 2 =0) with the generalized Leibbrandt-Mandelstam prescription is the tree-level action for a certain class of regulators. The Gauss linking number is expressed in terms of the axial propagators for the gauge fields.
12423687
Regularization and Renormalization of Chern-Simons Theory
The topological field theory most familiar both to physicists and to mathematicians is surely Chern-Simons theory.