Fuzzy spaces and new random matrix ensembles

Nair, V. P.; Polychronakos, Alexios P.; Tekel, Juraj

doi:10.1103/physrevd.85.045021

Cited by 32 publications

(64 citation statements)

References 23 publications

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“…Further applications of this technique are found in [5], see also [6][7][8]. The rewriting of the kinetic term was done by applying techniques from group theory, making the calculations somewhat cumbersome.…”

Section: Jhep11(2015)115mentioning

confidence: 99%

“…The second one is a bootstrapping method presented in [9], which is more robust and more easily implemented, and we will use this method in the following. The basic idea behind the bootstrapping method consists in choosing suitable differential operators D such that 6) and both O kin and O MT are invariant under Φ → ΩΦΩ † for Ω ∈ U(N ). Then the operators O kin and O MT can be pulled out of the integral and the equation…”

Section: Jhep11(2015)115mentioning

confidence: 99%

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The phase diagram of scalar field theory on the fuzzy disc

Rea¹,

Sämann²

2015

J. High Energ. Phys.

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Using a recently developed bootstrapping method, we compute the phase diagram of scalar field theory on the fuzzy disc with quartic even potential. We find three distinct phases with second and third order phase transitions between them. In particular, we find that the second order phase transition happens approximately at a fixed ratio of the two coupling constants defining the potential. We compute this ratio analytically in the limit of large coupling constants. Our results qualitatively agree with previously obtained numerical results.

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Section: Jhep11(2015)115mentioning

confidence: 99%

Section: Jhep11(2015)115mentioning

confidence: 99%

The phase diagram of scalar field theory on the fuzzy disc

Rea¹,

Sämann²

2015

J. High Energ. Phys.

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“…[52]), in a tridimensional version of the model [53,54], at finite temperature [55], in a multi-trace formulation [56,57], et c. 1 The results of these numerical simulations can be compared with several analytical studies, including refs. [5,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76].…”

Section: Results For Nc Scalar Field Theorymentioning

confidence: 99%

The numerical approach to quantum field theory in a noncommutative space

Panero¹

2016

Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015)

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Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is presented, and their implications are reviewed. In addition, we also discuss how related numerical techniques have been recently applied in computer simulations of dimensionally reduced supersymmetric theories.

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“…to the number N planar (2n) of planar contractions of a vertex with 2n legs. See also [45][46][47][48] for an alternative derivation.…”

Section: Introductionmentioning

confidence: 99%

“…See also [86] for a review and an extension of this method to the noncommutative Moyal-Weyl plane. For an earlier approach see [44] and for a similar more nonperturbative approach see [45][46][47][48]. This technique is expected to capture the matrix transition between disordered and non-uniform ordered phases with arbitrarily increasing accuracy by including more and more terms in the expansion.…”

Section: Introductionmentioning

confidence: 99%

Wilson RG of noncommutative Φ44

Ydri

Ahmim

Bouchareb

2015

Int. J. Mod. Phys. A

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We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large N . Three fixed points are identified. The matrix model θ = ∞ fixed point which describes the disordered-to-non-uniform-ordered transition. The Wilson-Fisher fixed point at θ = 0 which describes the disordered-to-uniformordered transition, and a noncommutative Wilson-Fisher fixed point at a maximum value of θ which is associated with the transition between non-uniform-order and uniform-order phases. IntroductionA noncommutative field theory is a non-local field theory in which we replace the ordinary local point-wise multiplication of fields with the non-local Moyal-Weyl star product [1,2]. This product is intimately related to coherent states [6][7][8], Berezin quantization [9] and deformation quantization [10]. It is also very well understood that the underlying operator/matrix structure of the theory, exhibited by the Weyl map [5], is the singular most important difference with commutative field theory since it is at the root cause of profound physical differences between the two theories. We suggest [3] and references therein for elementary and illuminating discussion of the Moyal-Weyl product and other star products and their relations to the Weyl map and coherent states.Noncommutative field theory is believed to be of importance to physics beyond the standard model and the Hall effect [34] and also to quantum gravity and string theory [35,36]. * Email:ydri@stp.dias.ie, badis.ydri@univ-annaba.org. 1Noncommutative scalar field theories are the most simple, at least conceptually, quantum field theories on noncommutative spaces. Some of the novel quantum properties of noncommutative scalar field theory and scalar phi-four theory are as follows:

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Fuzzy spaces and new random matrix ensembles

Cited by 32 publications

References 23 publications

The phase diagram of scalar field theory on the fuzzy disc

The phase diagram of scalar field theory on the fuzzy disc

The numerical approach to quantum field theory in a noncommutative space

Wilson RG of noncommutative Φ44

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