121689569
Dimensional regularisation of Chern-Simons field theory
Abstract We discuss the dimensional regularisation program as applied to a pure Chern-Simons theory in Minkowski space. In order to make this regularisation program feasible, we propose adding a Yang-Mills term to the pure Chern-Simons action. It is argued that the pure Chern-Simons theory is recovered in a certain limit. Explicit computations are carried out at the one-loop level in the background field gauge.
122604338
Nonlocalities in field theory
It has been known since the early 1980's that the computation of light-cone gauge Feynman integrals in the nμ∗ prescription yields both local and nonlocal ultraviolet divergences. Nevertheless, it was recently claimed that the nonlocal contributions to the Yang-Mills vacuum polarization tensor arise from application of the decomposition formula [q·n(q+p)·n]−1=(p·n)−1{−[(q+p)·n]−1+(q·n)−1}, p·n≠0. The purpose of this paper is to show that nonlocal ultraviolet divergences automatically appear in light-cone gauge Feynman integrals defined by the nμ∗ prescription, regardless whether the above decomposition formula is employed or not.
118725047
BRS techniques applied to the temporal-planar gauge with the vienna prescription: The dependence on the axial vectors
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.
120724746
DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES
We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.
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.
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.
120556867
Experimental tests of extra dimensions
Abstract Spherically symmetric solutions of general relativity in higher dimensions are tested. We find that the existence of extra dimensions is compatible with the classical tests of general relativity, which place almost no restrictions on the parameters involved. The models studied fail to explain the geological data concerning the apparent variability of the gravitational constant with the distance.
13961384
The one loop UV divergent structure of U(1) Yang-Mills theory on noncommutative R**4
We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized at the one-loop level by multiplicative dimensional renormalization of the coupling constant and fields of the theory. We compute the beta function of the theory and conclude that the theory is asymptotically free. We also show that the Weyl-Moyal matrix defining the deformed product over the space of functions on R^4 is not renormalized at the one-loop level.
18503987
Anomaly freedom in Seiberg-Witten noncommutative gauge theories
We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly calculating the epsilon(mu1mu2mu3mu4) part of the renormalized effective action, we first find the would-be one-loop anomaly of the theory to all orders in the noncommutativity parameter theta(munu). And secondly we isolate in the would-be anomaly radiative corrections which are not BRS trivial. This gives as the only true anomaly occurring in the theory the standard Bardeen anomaly of commutative spacetime, which is set to zero by the usual anomaly cancellation condition.
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.