Gauge Independence of IR singularities in Non-Commutative QFT - and Interpolating Gauges

IR divergences of a non-commutative U(1) Maxwell theory are discussed at the one-loop level using an interpolating gauge to show that quadratic IR divergences are independent not only from a covariant gauge fixing but also independent from an axial gauge fixing.Comment: 11 pages, 2 figures, v1 minor correction

Seiberg-Witten map for noncommutative super Yang-Mills theory

In this letter we derive the Seiberg-Witten map for noncommutative super Yang-Mills theory in Wess-Zumino gauge. Following (and using results of) hep-th/0108045 we split the observer Lorentz transformations into a covariant particle Lorentz transformation and a remainder which gives directly the Seiberg-Witten differential equations. These differential equations lead to a theta-expansion of the noncommutative super Yang-Mills action which is invariant under commutative gauge transformations and commutative observer Lorentz transformation, but not invariant under commutative supersymmetry transformations: The theta-expansion of noncommutative supersymmetry leads to a theta-dependent symmetry transformation. For this reason the Seiberg-Witten map of super Yang-Mills theory cannot be expressed in terms of superfields.Comment: 9 page

Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map

We show that the noncommutative Yang-Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The noncommutative Yang-Mills action is invariant under combined conformal transformations of the Yang-Mills field and of the noncommutativity parameter \theta. The Seiberg-Witten differential equation results from a covariant splitting of the combined conformal transformations and can be computed as the missing piece to complete a covariant conformal transformation to an invariance of the action.Comment: 20 pages, LaTeX. v2: Streamlined proofs and extended discussion of Lorentz transformation

One Loop Renormalizability of Spontaneously Broken Gauge Theory with a Product of Gauge Groups on Noncommutative Spacetime: the U(1) x U(1) Case

A generalization of the standard electroweak model to noncommutative spacetime would involve a product gauge group which is spontaneously broken. Gauge interactions in terms of physical gauge bosons are canonical with respect to massless gauge bosons as required by the exact gauge symmetry, but not so with respect to massive ones; and furthermore they are generally asymmetric in the two sets of gauge bosons. On noncommutative spacetime this already occurs for the simplest model of U(1) x U(1). We examine whether the above feature in gauge interactions can be perturbatively maintained in this model. We show by a complete one loop analysis that all ultraviolet divergences are removable with a few renormalization constants in a way consistent with the above structure.Comment: 24 pages, figures using axodraw; version 2: a new ref item [4] added to cite efforts to all orders, typos fixed and minor rewordin

Perturbative Chern-Simons Theory on Noncommutative R^3

A U(N) Chern-Simons theory on noncommutative $\mathbb{R}^{3}$ is constructed as a \q-deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that the theory is finite and \q_{\m\n}-independent at the one loop level and that the calculations respect the restriction of the topological supersymmetry. Thus the topological \q-deformed Chern-Simons theory is an example of a model which is non-singular in the limit \q \to 0.Comment: 10 pages, 3 figures. Added loop calculation, conclusions unchanged, some references adde

Non-commutative U(1) Super-Yang-Mills Theory: Perturbative Self-Energy Corrections

The quantization of the non-commutative N=1, U(1) super-Yang-Mills action is performed in the superfield formalism. We calculate the one-loop corrections to the self-energy of the vector superfield. Although the power-counting theorem predicts quadratic ultraviolet and infrared divergences, there are actually only logarithmic UV and IR divergences, which is a crucial feature of non-commutative supersymmetric field theories.Comment: 18 pages, latex, uses feynmf package; references added, Wess-Zumino gauge remove

On the energy-momentum tensor in non-commutative gauge theories

We study the properties of the energy-momentum tensor in non-commutative gauge theories by coupling them to a weak external gravitational field. In particular, we show that the stress tensor of such a theory coincides exactly with that derived from a theory where a Seiberg-Witten map has been implemented (namely, the procedure is commutative). Various other interesting features are also discussed.Comment: 3 page

Noncommutative Supersymmetry in Two Dimensions

Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the ${\cal N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane. The algebra is obtained using appropriate representaions of its generators on the space of superfields in a $D=2, {\cal N}=1$ ``noncommutative superspace.'' We find that the (anti)commutators between several (super)translation generators are no longer vanishing, but involve a new set of generators which together with the (super)translation and rotation generators form a consistent closed algebra. We then analyze the spectrum of this algebra in order to obtain its fundamental and adjoint representations.Comment: 30 pages, Latex, no figures, some modifications including change of notations and addition of some comment