Noncommutative scalar field theory in a curved background: duality between noncommutative and effective commutative description

We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner Nordstrom like background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action descri...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Ćirić, Marija Dimitrijević, Konjik, Nikola, Samsarov, Andjelo
Format: Article
Language:English
Subjects:
Deformation effects
Equations of motion
Field theory
Operators (mathematics)
Scalars
Online Access:Get full text
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Summary:We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner Nordstrom like background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action describing a NC scalar field minimally coupled to the RN geometry is manifestly invariant under the deformed U(1) gauge symmetry. We find the equation of motion and conclude that the same equation is obtained from the commutative theory in a modified geometrical background described by an effective metric. This correspondence we call duality between formal and effective approach. We also show that a NC deformation via semi Killing twist operator cannot be rewriten in terms of an effective metric. There is a dual description for those particular deformations.
ISSN:2331-8422