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Selfdual noncommutative φ4theory in four dimensions is a nonperturbatively solvable and nontrivial quantum field theory,” arXiv:1205.0465
"... in four dimensions is a nonperturbatively solvable and nontrivial quantum field theory ..."
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in four dimensions is a nonperturbatively solvable and nontrivial quantum field theory
Loop Vertex Expansion for Φ2k Theory in Zero Dimension
 Journal of Mathematical Physics
"... In this paper we extend the method of loop vertex expansion to interactions with degree higher than 4. As an example we provide through this expansion an explicit proof that the free energy of φ2k scalar theory in zero dimension is BorelLe Roy summable of order k−1. We detail the computations in t ..."
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Cited by 9 (5 self)
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In this paper we extend the method of loop vertex expansion to interactions with degree higher than 4. As an example we provide through this expansion an explicit proof that the free energy of φ2k scalar theory in zero dimension is BorelLe Roy summable of order k−1. We detail the computations in the case of a φ6 interaction.
Spectral geometry of the Moyal plane with harmonic propagation. arxiv 1108.2184
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Perturbative Quantum Field Theory via Vertex Algebras
, 2009
"... In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras. Our starting point is the WilsonZimmermann operator product expansion (OPE). Following ideas of a previous paper [arXiv:0802.2198], we consider a consistency (essentially as ..."
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Cited by 7 (2 self)
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In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras. Our starting point is the WilsonZimmermann operator product expansion (OPE). Following ideas of a previous paper [arXiv:0802.2198], we consider a consistency (essentially associativity) condition satisfied by the coefficients in this expansion. We observe that the information in the OPE coefficients can be repackaged straightforwardly into “vertex operators ” and that the consistency condition then has essentially the same form as the key condition in the theory of vertex algebras. We develop a general theory of perturbations of the algebras that we encounter, similar in nature to the Hochschild cohomology describing the deformation theory of ordinary algebras. The main part of the paper is devoted to the question how one can calculate the perturbations corresponding to a given interaction Lagrangian (such as λϕ 4) in practice, using the consistency condition and the corresponding nonlinear field equation. We derive graphical rules, which display the vertex operators (i.e., OPE coefficients) in terms of certain multiple series of hypergeometric type.
Non Commutative Field Theory on Rank One Symmetric Spaces,” arXiv:0806.4255 [hepth
"... Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary spacetime. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is taken to extend such theories to nonflat backgrounds such ..."
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Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary spacetime. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is taken to extend such theories to nonflat backgrounds such as solvable symmetric spaces. 1
Borel summability and the non perturbative 1/N expansion of arbitrary quartic tensor models
, 2014
"... We extend the proof of Borel summability of melonic quartic tensor models to tensor models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and new bounds based on CauchySchwarz inequalities. The Bo ..."
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Cited by 5 (1 self)
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We extend the proof of Borel summability of melonic quartic tensor models to tensor models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and new bounds based on CauchySchwarz inequalities. The Borel summability is proven to be uniform as the tensor size becomes large. Furthermore, we show that the 1/N expansion of any quartic tensor model can be performed at the constructive level, that is we show that every cumulant is a sum of explicit terms up to some order plus a rest term which is an analytic function in the coupling constant in a cardioid domain of the complex plane and which is suppressed in 1/N.
How are Feynman graphs resummed by the Loop Vertex Expansion, arXiv 1006
"... The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the φ4 theory in noninteger dimension. LPT20XXxx ..."
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Cited by 4 (4 self)
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The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the φ4 theory in noninteger dimension. LPT20XXxx
On the effective action of noncommutative Yang–Mills theory
 INTERNATIONAL CONFERENCE ON NONCOMMUTATIVE GEOMETRY AND PHYSICS
, 2007
"... We compute here the YangMills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar field theory with harmonic term, minimally coupled to an external gauge potential. We also explain the special regularisation scheme chosen here and give some links to the ..."
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We compute here the YangMills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar field theory with harmonic term, minimally coupled to an external gauge potential. We also explain the special regularisation scheme chosen here and give some links to the Schwinger parametric representation. Finally, we discuss the results obtained: a noncommutative possibly renormalisable YangMills theory.