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Article Dans Une Revue Annales de l'Institut Henri Poincare Physique Theorique Année : 2005

Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation Manifolds

Résumé

We work out the general features of perturbative field theory on noncommutative manifolds defined by isospectral deformation. These (in general curved) `quantum spaces\', generalizing Moyal planes and noncommutative tori, are constructed using Rieffel\'s theory of deformation quantization for action of $\\R^l$. Our framework, incorporating background field methods and tools of QFT in curved spaces, allows to deal both with compact and non-compact spaces, as well as with periodic or not deformations, essentially in the same way. We compute the quantum effective action up to one loop for a scalar theory, showing the different UV/IR mixing phenomena for different kinds of isospectral deformations. The presence and behavior of the non-planar parts of the Green functions is understood simply in terms of off-diagonal heat kernel contributions. For periodic deformations, a Diophantine condition on the noncommutativity parameters is found to play a role in the analytical nature of the non-planar part of the one-loop reduced effective action. Existence of fixed points for the action may give rise to a new kind of UV/IR mixing.

Dates et versions

hal-00005249 , version 1 (09-06-2005)

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Citer

Victor Gayral. Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation Manifolds. Annales de l'Institut Henri Poincare Physique Theorique, 2005, 6, pp.1-33. ⟨hal-00005249⟩
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