Loop calculations for the non-commutative U
                     ⋆(1) gauge field model with oscillator term

Blaschke, Daniel N.; Grosse, Harald; Kronberger, Erwin; Schweda, M.; Wohlgenannt, Michael

doi:10.1140/epjc/s10052-010-1295-5

Cited by 26 publications

(29 citation statements)

References 50 publications

(82 reference statements)

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“…This is mainly due to its complicated vacuum structure explored in [53] which excludes the use of any standard perturbative treatment. Other attempts to control the UV/IR mixing have been considered in [54,55] - [60]. However, showing that any of these models is renormalizable is still an open problem.…”

Section: Jhep09(2013)051mentioning

confidence: 99%

Noncommutative gauge theories on $ \mathbb{R}_{\theta}^2 $ as matrix models

Martinetti

Vitale

Wallet

2013

J. High Energ. Phys.

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We study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Expanding the action around symmetric vacua generates non local matrix models with polynomial interaction terms. For a particular vacuum, we can invert the kinetic operator which is related to a Jacobi operator. The resulting propagator can be expressed in terms of Chebyschev polynomials of second kind. We show that non vanishing correlations exist at large separations. General considerations on the kinetic operators stemming from the other class of symmetric vacua, indicate that only one class of symmetric vacua should lead to fast decaying propagators. The quantum stability of the vacuum is briefly discussed.

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Section: Jhep09(2013)051mentioning

confidence: 99%

Noncommutative gauge theories on $ \mathbb{R}_{\theta}^2 $ as matrix models

Martinetti

Vitale

Wallet

2013

J. High Energ. Phys.

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“…We expect our results can help in the involved perturbative study of these and similar models (see e.g. [77]).…”

Section: Discussionmentioning

confidence: 66%

U(N) Yang-Mills in non-commutative space time

Ahmadiniaz

Corradini

Edwards

et al. 2019

J. High Energ. Phys.

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We present an approach to U ⋆ (N) Yang-Mills theory in non-commutative space based upon a novel phase-space analysis of the dynamical fields with additional auxiliary variables that generate Lorentz structure and colour degrees of freedom. To illustrate this formalism we compute the quadratic terms in the effective action focusing on the planar divergences so as to extract the β-function for the Yang-Mills coupling constant. Nonetheless the method presented is general and can be applied to calculate the effective action at arbitrary order of expansion in the coupling constant, including both planar and non-planar contributions, and is well suited to the computation of low energy one-loop scattering amplitudes.

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“…Similar to the GW case, both star-commutators and anticommutators in theX µ appear in the resulting "induced" gauge field action, the commutator being related to the field strength via X µ ,X ν = igF µν − iθ −1 µν . Furthermore, starting from the naive NCGFT (3.4) and adding an oscillator type term in a BRS invariant way [87] leads to that same action at the one-loop level [88]. The main difficulty of the induced gauge field action lies in the vacuum structure which exhibits tadpoles and is not very well understood [89,90].…”

Section: Gauge Theoriesmentioning

confidence: 99%

Aspects of perturbative quantum field theory on non-commutative spaces

Blaschke

2016

Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015)

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In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces when constructing various scalar, fermionic and gauge field theories on Moyal space, and especially how the UV/IR mixing problem was solved for certain models. Finally, I outline more recent progress in constructing a renormalizable gauge field model on non-commutative space, and how one might attempt to prove renormalizability of such a model using a generalized renormalization scheme adapted to the non-commutative (and hence non-local) setting.

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Loop calculations for the non-commutative U ⋆(1) gauge field model with oscillator term

Cited by 26 publications

References 50 publications

Noncommutative gauge theories on $ \mathbb{R}_{\theta}^2 $ as matrix models

Noncommutative gauge theories on $ \mathbb{R}_{\theta}^2 $ as matrix models

U(N) Yang-Mills in non-commutative space time

Aspects of perturbative quantum field theory on non-commutative spaces

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