A Translation-Invariant Renormalizable Non-Commutative Scalar Model

Gurău, Razvan; Magnen, J. Le; Rivasseau, Vincent; Tanasă, Adrian

doi:10.1007/s00220-008-0658-3

Cited by 92 publications

(199 citation statements)

References 36 publications

(48 reference statements)

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“…As a summary, one can state that the action of a noncommutative scalar quantum field theory is defined in such a way that the bi-linear part may contain a non-local piece 1 2 φ 1 φ in order to obtain an IR damping for small k values -whereas the interaction terms are determined by the requirement of power counting renormalizability.…”

Section: Scalar Theorymentioning

confidence: 99%

“…Among the possibilities to avoid this problem and to make sense of the perturbative expansion, we want to focus on the one suggested by Gurau et al [1] 3 . They modified the bi-linear part of the classical action in the following way:…”

Section: Introductionmentioning

confidence: 99%

“…As a consequence, the high momentum behaviour remains unchanged, but the non-perturbative region (for small k-values) changes dramatically and avoids UV/IR mixing [1,3]. This modifications can be implemented by taking advantage of the fact that the non-commutativity parameter introduces a length scale and operators of the form or D 2D2 , respectively, where D denotes the covariant derivative, have mass dimension zero.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On noncommutative quantum field theories and dimensionless insertions

Schweda¹,

Wohlgenannt²

2011

J. Phys. A: Math. Theor.

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Section: Scalar Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On noncommutative quantum field theories and dimensionless insertions

Schweda¹,

Wohlgenannt²

2011

J. Phys. A: Math. Theor.

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“…These encompass the scalar φ 4 model with harmonic term on R 2 θ or R 4 θ [16][17][18], this latter being likely non-perturbatively solvable [19], the translational and rotational invariant related φ 4 models [20,21] together with fermionic versions [22,23] and solvable models inherited from the LSZ model [24]. The situation for the gauge theories is not so favorable.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative gauge theories on ℝ λ 3 $$ {\mathrm{\mathbb{R}}}_{\uplambda}^3 $$ : perturbatively finite models

Géré

Jurić²,

Wallet

2015

J. High Energ. Phys.

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We show that natural noncommutative gauge theory models on R 3 λ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of R 3 λ and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is discussed. Finally, the existence of a particular model related to integrable hierarchies is indicated, for which the partition function is expressible as a product of ratios of determinants.

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“…Perturbative analysis led to some noncommutative corrections but also, what is more important, to a quite universal property of NCFT -UV/IR mixing [6]. (Though, see some recent proposals on models without UV/IR mixing [7][8][9].) This property, which is due to the non-local nature of noncommutativity, put an end to hopes that noncommutativity (at least in the simple form of a constant θ µν ) would serve as a UV regulator, which was the major motivation for one of the first works on a NC space-time [10].…”

Section: Introductionmentioning

confidence: 99%

UV/IR mixing as a twisted Poincaré anomaly

Pinzul¹

2012

J. Phys. A: Math. Theor.

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We analyze symmetries of the 1-loop effective action of φ 4 noncommutative field theory. It is shown, that despite the twisted Poincaré invariance of the classical noncommutative action, its 1-loop quantum counterpart lacks this invariance. Though Noether analysis of the model is somewhat obscure, it is still possible to interpret this symmetry breaking as a quantum anomaly due to inappropriate choice of the quantization method. * apinzul@unb.br 1 IntroductionBased on a quite general argument [1], it is believed that one or another form of a noncommutative (NC) space-time should emerge as a quasi-classical approximation to quantum gravity in a sense that quantum fields on such a space-time will probe the quantum gravity scale through noncommutativity. This observation, as well as the appearance of NC field theory in super strings [2], sparked considerable interest in noncommutative physics. Most of the efforts have been devoted to the analysis of theories on a NC space-time with constant noncommutativity, a so-called Moyal space. (Literature on the subject is vast, for a review see, e.g. [3]) This is the simplest possible type of noncommutativity, defined by the following commutation relation between the coordinatesHere θ µν gives the scale of quantum gravity, usually it is thought to be related to the Planck scale. It is clear that if θ µν is some non-dynamical constant, which is the case in string theory, then (1) breaks Lorentz invariance.The study of Lorentz-breaking theories has a long history by now [4]. Up to the first order in θ µν , NC quantum field theory with constant noncommutativity is just a special case of the general situation (e.g., see discussion in [5]). The quantization of NC field theories (NCFT) had been performed within this framework, i.e quantization of a Lorentz violating theory. Perturbative analysis led to some noncommutative corrections but also, what is more important, to a quite universal property of NCFT -UV/IR mixing [6]. (Though, see some recent proposals on models without UV/IR mixing [7][8][9].) This property, which is due to the non-local nature of noncommutativity, put an end to hopes that noncommutativity (at least in the simple form of a constant θ µν ) would serve as a UV regulator, which was the major motivation for one of the first works on a NC space-time [10].After works [11,12], another possibility to look at NCFT had become possible: instead of thinking in terms of broken Lorentz invariance, one could now think about NCFT as a theory with preserved, but twisted Lorentz symmetry.1 On the classical level, this is just a point of view that does not add anything new to the picture. But the transition to quantization changes the situation drastically: one has to maintain this new twisted symmetry on quantum level. Essentially, there exist two approaches to quantization of NCFT with twisted Lorentz symmetry:• The quantization should be done according to the usual rules. In other words, the usual Feynman rules, derived from the path integral with the standard quant...

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A Translation-Invariant Renormalizable Non-Commutative Scalar Model

Abstract: Abstract:In this paper we propose a translation-invariant scalar model on the Moyal space. We prove that this model does not suffer from the UV/IR mixing and we establish its renormalizability to all orders in perturbation theory.

Cited by 92 publications

References 36 publications

On noncommutative quantum field theories and dimensionless insertions

On noncommutative quantum field theories and dimensionless insertions

Noncommutative gauge theories on ℝ λ 3 $$ {\mathrm{\mathbb{R}}}_{\uplambda}^3 $$ : perturbatively finite models

UV/IR mixing as a twisted Poincaré anomaly

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