Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences

2013

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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.

Section: Jhep09(2013)051mentioning

confidence: 69%

Section: Jhep09(2013)051mentioning

confidence: 76%

Section: The ω = 0 Casementioning

confidence: 85%

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

Martinetti

Vitale

2013

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“…true for alternative approaches based on a IR damping mechanism aiming to neutralize the mixing [44,45]. 2 Note however that the matrix model interpretation of noncommutative gauge theories provided interesting results on (semi-)classical properties and/or one-loop computations.…”

Section: Jhep05(2016)146mentioning

confidence: 99%

Closed star product on noncommutative ℝ 3 and scalar field dynamics

Jurić

Poulain

2016

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Abstract:We consider the noncommutative space R 3 θ , a deformation of R 3 for which the star product is closed for the trace functional. We study one-loop IR and UV properties of the 2-point function for real and complex noncommutative scalar field theories with quartic interactions and Laplacian on R 3 as kinetic operator. We find that the 2-point functions for these noncommutative scalar field theories have no IR singularities in the external momenta, indicating the absence of UV/IR mixing. We also find that the 2-point functions are UV finite with the deformation parameter θ playing the role of a natural UV cut-off. The possible origin of the absence of UV/IR mixing in noncommutative scalar field theories on R 3 θ as well as on R 3 λ , another deformation of R 3 , is discussed.

“…Unfortunately, its complicated vacuum structure explored in [36,37] forbids the use of any standard perturbative treatment. 1 Alternative based on the implementation of a IR damping mechanism have been proposed and studied [39][40][41][42]. Although this damping mechanism is appealing, it is not known if it can produce a renormalisable gauge theory on R 4 θ .…”

Section: Jhep12(2015)045mentioning

confidence: 99%

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

Géré

Jurić²,

2015

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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.