Michael Wohlgenannt

Induced gauge theory on a noncommutative space

We consider a scalar φ4 theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action, using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.

The standard model on non-commutative space-time: electroweak currents and the Higgs sector

Abstract.We review the electroweak charged and neutral currents in the non-commutative standard model (NCSM) and compute the Higgs and Yukawa parts of the NCSM action. With the aim to make the NCSM accessible to phenomenological considerations, all relevant expressions are given in terms of physical fields, and Feynman rules are provided.

The standard model on non-commutative space-time : strong interactions included

Abstract.This paper is a direct extension of our earlier work on electroweak currents and the Higgs sector in the standard model on non-commutative space-time, now with strong interactions included. Apart from the non-commutative corrections to standard model strong interactions, several new interactions appear. The most interesting ones are gluonic interactions with the electroweak sector. They are elaborated here in detail and the Feynman rules for interactions up to

Emergent gravity, matrix models and UV/IR mixing

{cal O}(g^2_s theta)

Translation-invariant models for non-commutative gauge fields

are provided.

On κ-deformation and UV/IR mixing

We verify explicitly that UV/IR mixing for noncommutative gauge theory can be understood in terms of an induced gravity action, as predicted by the identification [1] of gravity within matrix models of NC gauge theory. More precisely, we obtain the Einstein-Hilbert action by integrating out a scalar field in the adjoint. It arises from the well-known UV/IR mixing of NC gauge theory, which is carefully re-analyzed and interpreted in terms of gravity. The matrix model therefore contains gravity as an IR effect, due to UV/IR mixing.

Scalar field propagation in the ϕ4κ-Minkowski model

Motivated by the recent construction of a translation-invariant renormalizable non-commutative model for a scalar field [1], we introduce models for non-commutative U(1) gauge fields along the same lines. More precisely, we include some extra terms into the action with the aim of getting rid of the UV/IR mixing.

Noncommutative QFT and renormalization

We examine the UV/IR mixing property on a κ-deformed Euclidean space for a real scalar ϕ4 theory. All contributions to the tadpole diagram are explicitly calculated. UV/IR mixing is present, though in a different dressing than in the case of the canonical deformation.

Heat kernel expansion and induced action for the matrix model Dirac operator

A bstractIn this article we use the noncommutative (NC) κ-Minkowski ϕ4 model based on the κ-deformed star product, (★h). The action is modified by expanding up to linear order in the κ-deformation parameter a, producing an effective model on commutative spacetime. For the computation of the tadpole diagram contributions to the scalar field propagation/self-energy, we anticipate that statistics on the κ-Minkowski is specifically κ-deformed. Thus our prescription in fact represents hybrid approach between standard quantum field theory (QFT) and NCQFT on the κ-deformed Minkowski spacetime, resulting in a κ-effective model. The propagation is analyzed in the framework of the two-point Green’s function for low, intermediate, and for the Planckian propagation energies, respectively. Semiclassical/hybrid behavior of the first order quantum correction do show up due to the κ-deformed momentum conservation law. For low energies, the dependence of the tadpole contribution on the deformation parameter a drops out completely, while for Planckian energies, it tends to a fixed finite value. The mass term of the scalar field is shifted and these shifts are very different at different propagation energies. At the Planck-ian energies we obtain the direction dependent κ-modified dispersion relations. Thus our κ-effective model for the massive scalar field shows a birefringence effect.

On the renormalization of non-commutative field theories

Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to