121471524
UV-divergent part of the vacuum polarization tensor in the temporal gauge with the LM prescription. BRS identities
Abstract The one-loop UV-divergent contribution to the vacuum polarization tensor (Πμνab) is computed in a temporal-planar gauge using the LM prescription that gives the correct exponential behaviour for the Wilson loop. Its dependence on the gauge parameter and on the magnitude of the unphysical vectors n and n′ - introduced by the LM prescription - is derived from the BRS invariance of the theory and shown to be consistent with our result for Πabμν.
10342426
Physically meaningful and not so meaningful symmetries in Chern-Simons theory.
We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action that is both Becchi-Rouet-Stora (BRS) invariant and Landau supersymmetric and an effective action that is only BRS invariant is a finite field redefinition. Having established this, we use a BRS-invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift [ital k][r arrow][ital k]+[ital c][sub [ital V]] of the bare Chern-Simons parameter [ital k] in connection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS-invariant regulators used as yet yield the same value for the shift.
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.
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.
118725047
BRS techniques applied to the temporal-planar gauge with the vienna prescription: The dependence on the axial vectors
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.
16068559
Abelian Chern-Simons theory as the strong large-mass limit of topologically massive abelian gauge theory: the Wilson loop
Abstract We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in R 3 can be defined so that its large-mass limit is the renormalized vacuum expectation value of the Wilson loop for abelian Chern-Simons theory also in R 3 .
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.
8691879
Gauge Invariant Variables for SU ( 2 ) Yang-Mills Theory
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.
118345116
Computing the $\theta$-exact Seiberg-Witten map for arbitrary gauge groups
We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in the gauge coupling constant or, equivalently, in the number of ordinary gauge fields. We do so for arbitrary compact gauge groups in arbitrary unitary representations. For gauge and matter fields, we fully work out \theta-exact non-hybrid Seiberg-Witten maps up to order three in the number of ordinary gauge fields.
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.