18871973
Noncommutative SU(N) theories, the axial anomaly, Fujikawa's method and the Atiyah-Singer index
Abstract Fujikawa's method is employed to compute at first order in the noncommutative parameter the U ( 1 ) A anomaly for noncommutative SU ( N ) . We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ μ ν , which is of “magnetic” type. Our results for SU ( N ) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.
16042630
CHIRAL GAUGE ANOMALIES ON NONCOMMUTATIVE MINKOWSKI SPACE–TIME
Chiral gauge anomalies on noncommutative Minkowski space–time are computed and have their origin elucidated. The consistent form and the covariant form of the anomaly are obtained. Both Fujikawa's method and Feynman diagram techniques are used to carry out the calculations.
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.
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.
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.
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.
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.
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.
116367467
The Shift of the Chern-Simons parameter beyond one loop