Commutative limit of a renormalizable noncommutative model

Magnen, J. Le; Rivasseau, Vincent; Tanasă, Adrian

doi:10.1209/0295-5075/86/11001

Cited by 20 publications

(32 citation statements)

References 39 publications

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“…GFT includes spin foams and LQG but it is a Lagrangian field theory on a group manifold; therefore, its renormalization properties can be tested either perturbatively (which constrains the forms of the kinetic term allowed by renormalizability) [178][179][180][181] or nonperturbatively via the functional renormalization approach [182][183][184][185]. Also the other major theories discussed in this review are based on perturbative fieldtheory renormalization, although in very different forms: examples are perturbative superstring theory (genus-expansion series of Riemann surfaces) [186][187][188][189][190][191][192][193][194][195][196], noncommutative field theory (nonplanar graphs) [197][198][199][200][201][202][203][204][205], nonlocal gravity (traditional QFT but with nonlocal operators) [31,33,37,38], and Hořava-Lifshitz gravity (traditional QFT but with higher-order Laplacians) [206].…”

Section: Quantum Gravitymentioning

confidence: 99%

Multifractional theories: an unconventional review

Calcagni

2017

J. High Energ. Phys.

323

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We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent flow-equation theorem on dimensional flow in quantum gravity, in particular its enormous impact on the multifractional paradigm. We will also get some new theoretical results about the construction of multifractional derivatives and the symmetries in the yet-unexplored theory $T_\gamma$, the resolution of ambiguities in the calculation of the spectral dimension, the relation between the theory $T_q$ with $q$-derivatives and the theory $T_\gamma$ with fractional derivatives, the interpretation of complex dimensions in quantum gravity, the frame choice at the quantum level, the physical interpretation of the propagator in $T_\gamma$ as an infinite superposition of quasiparticle modes, the relation between multifractional theories and quantum gravity, and the issue of renormalization, arguing that power-counting arguments do not capture the exotic properties of extreme UV regimes of multifractional geometry, where $T_\gamma$ may indeed be renormalizable. A careful discussion of experimental bounds and new constraints are also presented.Comment: 1+106 pages, 3 figures, 9 tables, 245 references. Review article (with several important novelties) through 72 questions; in some of them, there is text overlap with papers by the author, all indicated in the text. v2: references added, minor typos corrected, answers to questions 01, 59 and 68 expanded. v3: minor typos correcte

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Section: Quantum Gravitymentioning

confidence: 99%

Multifractional theories: an unconventional review

Calcagni

2017

J. High Energ. Phys.

323

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“…Concerning the quantum corrections for the model under consideration, we note the quite recent work [16,17,18] which is complementary to our study: the second work is devoted to the calculation of the one-loop beta function and to the parametric representation of Feynman amplitudes (according to the topology of the considered graphs). The approach of references [16,17] is based on the assumption that 4a…”

Section: Discussionmentioning

confidence: 91%

Quantum corrections for translation-invariant renormalizable non-commutative ϕ⁴theory

Blaschke

Gieres

Kronberger

et al. 2008

J. High Energy Phys.

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In this paper we elaborate on the translation-invariant renormalizable φ 4 theory in 4-dimensional non-commutative space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and higher orders we illustrate the mechanism which overcomes the UV/IR mixing problem and ultimately leads to a renormalizable model. The obtained results show that the IR divergences are also suppressed in the massless case, which is of importance for the gauge field theoretic generalization of the scalar field model.

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“…In principle the quantum corrections in NCQFTs are extremely profound, revealing a structure of pathological terms far beyond that found in ordinary field theories. For practical purposes, perturbative loop computation was the most intensively studied for the Moyal-Weyl (constant θ µν ) type deformation [16,17,28,32,50], for its preservation of translation invariance allows a (modified) Feynman diagrammatic calculation. Much of efforts went in taming divergences related to the ultraviolet-infrared connection/mixing, see for example [15,38,40,41,56,60].…”

Section: Discussionmentioning

confidence: 99%

“…Precisely, in [15,60,56] it was shown for the first time how UV short distance effects, considered to be irrelevant, could alter the IR dynamics, thus becoming known as the UV/IR mixing. Some significant progress on UV/IR mixing and related issues has been achieved [16,17,32,50,58] while a proper understanding of loop corrections is still sought for.…”

Section: Introductionmentioning

confidence: 99%

Two-Point Functions on Deformed Spacetime

Trampetić¹

2014

SIGMA

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Abstract. We present a review of the one-loop photon (Π) and neutrino (Σ) two-point functions in a covariant and deformed U(1) gauge-theory on the 4-dimensional noncommutative spaces, determined by a constant antisymmetric tensor θ µν , and by a parameter-space (κ f , κ g ), respectively. For the general fermion-photon S f (κ f ) and photon self-interaction S g (κ g ) the closed form results reveal two-point functions with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(µ 2 (θp) 2 ). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon two-point function in the 4-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of θ µν and setting deformation parameters (κ f , κ g ) = (0, 3). In this case the neutrino two-point function vanishes. Thus for a specific point (0, 3) in the parameter-space (κ f , κ g ), a covariant θ-exact approach is able to produce a divergencefree result for the one-loop quantum corrections, having also both well-defined commutative limit and point-like limit of an extended object.

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Commutative limit of a renormalizable noncommutative model

Cited by 20 publications

References 39 publications

Multifractional theories: an unconventional review

Multifractional theories: an unconventional review

Quantum corrections for translation-invariant renormalizable non-commutative ϕ⁴theory

Two-Point Functions on Deformed Spacetime

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Commutative limit of a renormalizable noncommutative model

Cited by 20 publications

References 39 publications

Multifractional theories: an unconventional review

Multifractional theories: an unconventional review

Quantum corrections for translation-invariant renormalizable non-commutative ϕ4theory

Two-Point Functions on Deformed Spacetime

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Product

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Quantum corrections for translation-invariant renormalizable non-commutative ϕ⁴theory