On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review

Arnold Rofner; Daniel N. Blaschke; Erwin Kronberger; Manfred Schweda; Michael Wohlgenannt; Rene I.P. Sedmik

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On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review

Daniel N. Blaschke, Erwin Kronberger, Arnold Rofner, Manfred Schweda, Rene I.P. Sedmik, Michael Wohlgenannt

High Energy Physics - Theory · Submitted 4 Aug 2009

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The authors' main claim In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.

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arXiv ID0908.0467 (version 2)

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CitationArnold Rofner, Daniel N. Blaschke, Erwin Kronberger, Manfred Schweda, Michael Wohlgenannt, Rene I.P. Sedmik. "On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review." arXiv:0908.0467 (2009). https://pith.science/paper/BAXYOEWM

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When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories on four-dimensional Euclidean Groenewold-Moyal deformed space, also known as `theta-deformed space'. In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem.	background 1.00	0.05	0.04	asserted 0.98
s1	So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories on four-dimensional Euclidean Groenewold-Moyal deformed space, also known as `theta-deformed space'.	background 0.71	0.05	0.06	asserted 1.00
s2	In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.	contribution 1.00	0.77	0.21	asserted 0.57

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Original abstract

When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories on four-dimensional Euclidean Groenewold-Moyal deformed space, also known as `theta-deformed space'. In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.

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12 arXiv papers cite this in 19 sentences

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Nonetheless, the authors claim to have shown renormalizability using Algebraic Renormalization, which as we have discussed in [ref] may not be applicable in theories.

One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model · Discussion · contest 0.78

Cites it as background 8 papers

Quantum field theories on spaces, in particular on Moyal space, have been studied for some time (for a review see [ref] and references therein), and although problems preventing successful renormalization have been overcome in the scalar cases, such as the Grosse-Wulkenhaar model [ref] and the translation invariant $1/p^2$-model by Gurau [ref] , gauge theories have so far eluded us [ref] : Even though some propositions how to restore renormalizability in those cases have been put forward, there exists no proof for their renormalizability.

Gauge Fields on Non-Commutative Spaces and Renormalization · Introduction · 0.97
There are various proposals which we recall briefly here, for more detailed reviews see [ref] .

Gauge fields on noncommutative geometries with curvature · Introduction · 0.96
For a detailed discussion we would like to refer to our recent article [ref] .

One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model · Symmetries · 0.86

What it cites · 70 sentences without a confident label

Cites as support 11 papers

Indeed, the form of eq:IR-div cannot simply be generated by contracting $F_$ with $θ_$ [ref] but requires `fine tuning' of the action.

Translation-invariant models for non-commutative gauge fields · Are non-commutative gauge theories feasible? · 0.99
The reason, as in the naïve scalar case, is that one finds a quadratic IR divergence in the non-planar part of the self-energy (which is independent of the gauge fixing [ref] ).

Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4 · Are non-commutative gauge theories feasible? · 0.99
It has been shown [ref] that only enveloping algebras, such as $U(N)$ or $O(N)$ and $USp(2N)$, survive the introduction of a deformed product (in the sense that commutators of algebra elements are again algebra elements), while e.g. $SU(N)$ does not.

Restrictions on Gauge Groups in Noncommutative Gauge Theory · Are non-commutative gauge theories feasible? · 0.99

Cites as background 10 papers

Ever since the first quantum field theory models were constructed, the greatest obstacle has been the infamous so-called problem [ref] , where certain types of Feynman graphs, the non-planar graphs, exhibit new unrenormalizable IR singularities in exceptional momenta (see [ref] for a review).

Non-commutative Renormalization · Introduction · 0.91
Ever since the first quantum field theory models were constructed, the greatest obstacle has been the infamous so-called problem [ref] , where certain types of Feynman graphs, the non-planar graphs, exhibit new unrenormalizable IR singularities in exceptional momenta (see [ref] for a review).

Noncommutative Field Theory · Introduction · 0.91
Ever since the first quantum field theory models were constructed, the greatest obstacle has been the infamous so-called problem [ref] , where certain types of Feynman graphs, the non-planar graphs, exhibit new unrenormalizable IR singularities in exceptional momenta (see [ref] for a review).

Quantum Field Theory on Noncommutative Spaces · Introduction · 0.91

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