Continuous point symmetries in group field theories

Kegeles, Alexander; Oriti, Daniele

doi:10.1088/1751-8121/aa5c14

Cited by 9 publications

(9 citation statements)

References 99 publications

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“…It is an interesting question to list the classical symmetries of the models + and × given by the generalized Noether theorem for such non-local theories [99,98]. To apply the Lie symmetry algorithm as worked out in these references could be an interesting exercise for derivative coupling theories and could bear important consequences for the Ward identities.…”

Section: Enhanced P 2a φ 4 Tensor Field Theoriesmentioning

confidence: 99%

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Renormalizable enhanced tensor field theory: The quartic melonic case

Geloun

Toriumi

2018

Journal of Mathematical Physics

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Amplitudes of ordinary tensor models are dominated at large N by the so-called melonic graph amplitudes. Enhanced tensor models extend tensor models with special scalings of their interactions which allow, in the same limit, that the sub-dominant amplitudes to be "enhanced", that is to be as dominant as the melonic ones. These models were introduced to explore new large N limits and to probe different phases for tensor models. Tensor field theory is the quantum field theoretic counterpart of tensor models and enhanced tensor field theory enlarges this theory space to accommodate enhanced tensor interactions. We undertake the multi-scale renormalization analysis for two types of enhanced quartic melonic theories with rank d tensor fields φ : (U (1) D ) d → C and with interactions of the form p 2a φ 4 reminiscent of derivative couplings expressed in momentum space. Scrutinizing the degree of divergence of both theories, we identify generic conditions for their renormalizability at all orders of perturbation. For a first type of theory, we identify a 2-parameter space of just-renormalizable models for generic (d, D). These models have dominant non-melonic four-point functions. Finally, by specifying the parameters, we detail the renormalization analysis of a second type of model. Lying in between just-and super-renormalizability, that model is more exotic: all four-point amplitudes are convergent, however it exhibits an infinite family of divergent two-point amplitudes.

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Section: Enhanced P 2a φ 4 Tensor Field Theoriesmentioning

confidence: 99%

“…where ∈f α is small (α ∼ O( 1 |p fs | 2ξ ) ∼ M −(2ξ)i ). We insert that expansion for each external face in (99) and obtain:…”

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confidence: 99%

Renormalizable enhanced tensor field theory: The quartic melonic case

Geloun

Toriumi

2018

Journal of Mathematical Physics

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“…The most important results in determining explicit solutions of nonlinear partial differential equations (NLPDEs) were derived in [1]. These types of methods are best known as continuous symmetry transformation groups [2][3][4][5][6]. At present, we use computer software (e.g., Maple, Mathematica) to make this kind of transformation.…”

Section: Introductionmentioning

confidence: 99%

Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions

Khater

Attia

2018

MCA

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In this article, we present a modified auxiliary equation method. We harness this modification in three fundamental models in the biological branch of science. These models are the biological population model, equal width model and modified equal width equation. The three models represent the population density occurring as a result of population supply, a lengthy wave propagating in the positive x-direction, and the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes, respectively. We discuss these models in nonlinear fractional partial differential equation formulas. We used the conformable derivative properties to convert them into nonlinear ordinary differential equations with integer order. After adapting, we applied our new modification to these models to obtain solitary solutions of them. We obtained many novel solutions of these models, which serve to understand more about their properties. All obtained solutions were verified by putting them back into the original equations via computer software such as Maple, Mathematica, and Matlab.

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“…A second option is to encode metric degrees of freedom in additional data associated to Feynman graphs. This strategy is sometimes called group field theory (GFT) [5,6,7,33,104,116,117,118,121] and has proven quite successful. In GFT one considers tensors over some Lie group that are furthermore invariant under the diagonal action of the group.…”

Section: R Guraumentioning

confidence: 99%

Invitation to Random Tensors

Gurău¹

2016

SIGMA

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Abstract. This article is preface to the SIGMA special issue "Tensor Models, Formalism and Applications", http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions. Why random tensors?General relativity, or classical gravity, is a theory of the ambient space-time geometry. The electroweak and strong interactions, that is the other three fundamental forces in nature, are described by perturbatively renormalizable quantum field theory [68,72,73,74,124,132,142,145] living on this geometric background. The main lesson of general relativity is that the ambient geometry is dynamical, and the main lesson of quantum field theory is that all the dynamical fields must be quantized. Thus, classical gravity predicts its own demise: a more fundamental theory, "quantum gravity", must come into play at some high energy scale.While classical general relativity is a field theory, it cannot be quantized the same way the standard model is: general relativity is not perturbatively renormalizable [70,143]. The lack of perturbative renormalizability of general relativity is a clear indicator that "quantum gravity" is quite different from the classical theory of gravity. This is why minimalistic approaches should be taken with a grain of salt: gravity is weakly coupled in the infrared, hence strongly coupled in the ultraviolet. This suggest that the fundamental degrees of freedom of quantum gravity are quite different from the geometric degrees of freedom perceived by low energy observers. It is far more likely that the geometric infrared degrees of freedom are just bound states of the genuine quantum gravity ultraviolet degrees of freedom.Over the years several candidate quantum gravity theories have been developed, most notably string theory. While much remains to be learned about the elusive fundamental theory of quantum gravity, one thing is certain: whatever this theory may be, it must make sense of an expression like:

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Continuous point symmetries in group field theories

Cited by 9 publications

References 99 publications

Renormalizable enhanced tensor field theory: The quartic melonic case

Renormalizable enhanced tensor field theory: The quartic melonic case

Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions

Invitation to Random Tensors

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