Noncommutative induced gauge theories on Moyal spaces

Wallet, Jean-Christophe

doi:10.1088/1742-6596/103/1/012007

Cited by 31 publications

(42 citation statements)

References 47 publications

(121 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present paper, we consider as in [55] the differential calculus generated by the Lie algebra of real inner derivations of R 3 12) where the inner derivation D µ satisfy the following commutation relation 15) where the X i 's are elements of G and |σ| is the signature of the permutation σ ∈ S p+q . Let M denotes a right-module over R 3 λ .…”

Section: Jhep12(2015)045mentioning

confidence: 99%

See 1 more Smart Citation

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

Géré

Jurić²,

Wallet

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: Jhep12(2015)045mentioning

confidence: 99%

“…NCFT on noncommutative Moyal spaces received a lot of attention from the end of the 90's, in particular from the viewpoint of perturbative properties and renormalisability [10][11][12]. For reviews, see for instance [13][14][15].…”

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.

View full text Add to dashboard Cite

show abstract

“…Some detailed studies of the Moyal NC algebra are carried out e.g in [8,9] while mathematical descriptions of the NC framework underlying the present study can be found in [37,21].…”

Section: Basic Featuresmentioning

confidence: 99%

“…Here, A µ denotes the so called covariant coordinates defined in section 2, a natural gauge covariant tensorial form stemming from the existence of a canonical gauge invariant connection within the present NC framework (for more details on the relevant mathematical structures see e.g in [36,37,21]. In (1.2), the additional 2nd term may be viewed as a "gauge counterpart" of the harmonic term introduced in [15].…”

mentioning

confidence: 99%

On the vacuum states for non-commutative gauge theory

2008

View full text Add to dashboard Cite

Candidates for renormalisable gauge theory models on Moyal spaces constructed recently have non trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which form a global symmetry group for the action. We compute the explicit expression in the position space for these vacuum configurations in two and four dimensions.

show abstract

“…Once the noncommutative nature of space-time is assumed which is generally reflected into the noncommutativity of an algebra of coordinates, noncommutative field theories (NCFT) or noncommutative gauge theories naturally arise. For reviews on early studies, see e.g [10][11][12] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Involutive representations of coordinate algebras and quantum spaces

Jurić

Poulain

Wallet

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

We show that su(2) Lie algebras of coordinate operators related to quantum spaces with su(2) noncommutativity can be conveniently represented by SO(3)-covariant poly-differential involutive representations. We show that the quantized plane waves obtained from the quantization map action on the usual exponential functions are determined by polar decomposition of operators combined with constraint stemming from the Wigner theorem for SU(2). Selecting a subfamily of * -representations, we show that the resulting star-product is equivalent to the Kontsevich product for the Poisson manifold dual to the finite dimensional Lie algebra su(2). We discuss the results, indicating a way to extend the construction to any semi-simple non simply connected Lie group and present noncommutative scalar field theories which are free from perturbative UV/IR mixing.

show abstract

Noncommutative induced gauge theories on Moyal spaces

Cited by 31 publications

References 47 publications

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

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

On the vacuum states for non-commutative gauge theory

Involutive representations of coordinate algebras and quantum spaces

Contact Info

Product

Resources

About