No abstract

A variation on the abelian Higgs model, with SU(2) global × U(1) local symmetry broken to U(1) global , was recently shown by Vachaspati and Achúcarro [1] to admit stable, finite energy cosmic string solutions even though the manifold of minima of the potential energy does not have non-contractible loops. Here we describe the most general solutions in the Bogomol'nyi limit, both in the single vortex case and the multi-vortex case. The single vortex solution depends on one complex parameter and coincides with that of Hindmarsh [2]; it may be regarded as a hybrid of a Nielsen-Olesen vortex and a CP 1 lump. The gravitational field of the vortices considered as cosmic strings is also obtained. Finally, monopole-like solutions interpolating between a Dirac monopole and a global monopole surrounded by an event horizon are found.2

We study quantum Chern-Simons theory as the large mass limit of the limit D → 3 of dimensionally regularized topologically massive YangMills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a highercovariant derivative Yang-Mills term plus dimensional regularization.Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift k → k + c V , k being the bare ChernSimons parameter. In passing we also prove by explicit computation that topologically massive Yang-Mills theory is UV finite.2

We compute the beta function at one loop for Yang-Mills theory using as regulator the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Faddeev and Slavnov. This regularization prescription has the appealing feature that it is manifestly gauge invariant and essentially four-dimensional. It happens however that the one-loop coefficient in the beta function that it yields is not −11/3, as it should be, but −23/6. The difference is due to unphysical logarithmic radiative corrections generated by the Pauli-Villars determinants on which the regularization method is based. This no-go result discards the prescription as a viable gauge invariant regularization, thus solving a long-standing open question in the literature. We also observe that the prescription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance.

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 ǫ µ 1 µ 2 µ 3 µ 4 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 θ µν . 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.

It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already at one loop order and suggests supersymmetrization and reinvestigating other types of noncommutativity.Comment: 1+7 pages. v2: two references adde

U(1) gauge theory on non-commutative Minkowski space-time in the Feynman-'t Hooft background gauge is studied. In particular, UV divergences and non-commutative IR divergent contributions to the two, three and four-point functions are explicitly computed at one loop. We show that the negative sign of the beta function results from paramagnetism -producing UV charge anti-screening-prevailing over diamagnetism -giving rise toUV charge screening. This dominance in the field theory setting corresponds to tachyon magnification dominance in the string theory framework. Our calculations provide an explicit realization of UV/IR mixing and lead to an IR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.

We look in Euclidean R 4 for associative star products realizing the commutation relation [x µ , x ν ] = iΘ µν (x), where the noncommutativity parameters Θ µν depend on the position coordinates x. We do this by adopting Rieffel's deformation theory (originally formulated for constant Θ and which includes the Moyal product as a particular case) and find that, for a topology R 2 × R 2 , there is only one class of such products which are associative. It corresponds to a noncommutativity matrix whose canonical form has components Θ 12 = −Θ 21 = 0 and Θ 34 = −Θ 43 = θ(x 1 , x 2 ), with θ(x 1 , x 2 ) an arbitrary positive smooth bounded function. In Minkowski space-time, this describes a position-dependent spacelike or magnetic noncommutativity. We show how to generalize our construction to n ≥ 3 arbitrary dimensions and use it to find traveling noncommutative lumps generalizing noncommutative solitons discussed in the literature. Next we consider Euclidean λφ 4 field theory on such a noncommutative background. Using a zeta-like regulator, the covariant perturbation method and working in configuration space, we explicitly compute the UV singularities. We find that, while the two-point UV divergences are non-local, the four-point UV divergences are local, in accordance with recent results for constant Θ.