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Noncommutative gauge theories on R^3_λ : Perturbatively finite models

Gere, Antoine; Jurić, Tajron; Wallet, Jean-Christophe
Noncommutative gauge theories on R^3_λ : Perturbatively finite models // The Journal of high energy physics, (2015), 12; 045-1 doi:10.1007/JHEP12(2015)045 (međunarodna recenzija, članak, znanstveni)

Noncommutative gauge theories on R^3_λ : Perturbatively finite models

Gere, Antoine ; Jurić, Tajron ; Wallet, Jean-Christophe

The Journal of high energy physics (1126-6708) (2015), 12; 045-1

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Non-Commutative Geometry ; Differential and Algebraic Geometry ; Matrix Models ; Models of Quantum Gravity

We show that natural noncommutative gauge theory models on R3λ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of R3λ 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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Znanstvena područja


Projekt / tema
HRZZ-IP-2014-09-9582 - prema kvantnoj gravitaciji: nekomutativna geometrija, teorija polja i kozmologija (Stjepan Meljanac, )

Institut "Ruđer Bošković", Zagreb

Autor s matičnim brojem:
Tajron Jurić, (330293)

Časopis indeksira:

  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus