Phase transition in gauge theories and multiple-point model

Лаперашвили, Л. В.; Nielsen, Holger Bech; Ryzhikh, D. A.

doi:10.1134/1.1451954

Cited by 9 publications

(25 citation statements)

References 47 publications

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“…Several attempts of connecting the geometry with the algebra have also been made [24][25][26][27]. Symmetries corresponding to higher dimensional lattices, like Z 5 , have been studied in the context of grand unified theories [28,29]. From our preliminary results, we can draw some general parallels with results from the particle physics and quantum field theories, but these connections remain open to further exploration and constitute the subject of future planned research.…”

Section: The End Game-discussion and Outlookmentioning

confidence: 72%

Non-Local Game of Life in 2D Quasicrystals

et al. 2018

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On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large number of tiles at all distances, the empires. Considering the emperor and its local patch as a quasiparticle, in this case a glider, its empire represents its field and the interaction between quasiparticles can be modeled as the interaction between their empires. Following a set of rules, we model the walk of life in different setups and we present examples of self-interaction and two-particle interactions in several scenarios. This dynamic is influenced by both higher dimensional representations and local choice of hinge variables. We discuss our results in the broader context of particle physics and quantum field theory, as a first step in building a geometrical model that bridges together higher dimensional representations, quasicrystals and fundamental particles interactions.

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Section: The End Game-discussion and Outlookmentioning

confidence: 72%

Non-Local Game of Life in 2D Quasicrystals

et al. 2018

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“…But in Refs. [22][23][24][25][26][27][28][29] instead of using the lattice or Wilson loop cut-off we have considered the Higgs Monopole Model (HMM) approximating the lattice artifact monopoles as fundamental point-like particles described by the Higgs scalar fields. Considering the renormalization group improvement of the effective Coleman-Weinberg potential [36,37], written in Ref.…”

Section: The Higgs Monopole Model and Phase Transitionmentioning

confidence: 99%

“…The next Subsections follow the review of the HMM calculations of the U(1) critical couplings obtained in Refs. [23][24][25].…”

Section: The Higgs Monopole Model and Phase Transitionmentioning

confidence: 99%

“…It was shown in Refs. [22][23][24][25][26][27][28][29] that one can crudely calculate the phase transition couplings without using any specific lattice, rather only approximating the lattice artifact monopoles as fundamental (point-like) magnetically charged particles condensing. Thus, the details of the lattice -hypercubic or random, with multiplaquette terms or without them, etc., -also the details of the regularization -lattice or Wilson loops, lattice or the Higgs monopole model -do not matter for values of the phase transition couplings so much.…”

Section: Approximate Universality Of the Critical Coupling Constantsmentioning

confidence: 99%

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Phase Transition in Gauge Theories, Monopoles and the Multiple Point Principle

Das

Лаперашвили

2005

Int. J. Mod. Phys. A

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This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model (FRGGM) and phase transitions in gauge theories with/without monopoles. Using renormalization group equations for the SM, the effective potential in the two-loop approximation is investigated, and the existence of its postulated second minimum at the fundamental scale is confirmed. Phase transitions in the lattice gauge theories are reviewed. The lattice results for critical coupling constants are compared with those of the Higgs monopole model, in which the lattice artifact monopoles are replaced by the point-like Higgs scalar particles with magnetic charge. Considering our (3 + 1)-dimensional space-time as, in some way, discrete or imagining it as a lattice with a parameter a = λ P , where λ P is the Planck length, we have investigated the additional contributions of monopoles to the β-functions of renormalization group equations for running fine structure constants α i (µ) (i = 1, 2, 3 correspond to the U (1), SU (2) and SU (3) gauge groups of the SM) in the FRGGM extended beyond the SM at high energies. It is shown that monopoles have N f am times smaller magnetic charge in the FRGGM than in the SM (N f am is a number of families in the FRGGM). We have estimated also the enlargement of a number of fermions in the FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have reviewed that, in contrast to the case of the Anti-grand unified theory (AGUT), there exists a possibility of unification of all gauge interactions (including gravity) near the Planck scale due to monopoles. The possibility of the [SU (5)] 3 or [SO(10)] 3 unification at the GUT-scale ∼ 10 18 GeV is briefly considered.

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“…In Refs. [17,18] the MPP was applied to the investigation of phase transitions in regularized gauge theories. It was shown in [19] that MPP forbids the existence of a fourth generation.…”

Section: Introduction: Cosmological Constant and Multiplepoint Principlementioning

confidence: 99%

The fundamental-electroweak scale hierarchy in the standard model

Froggatt

Laperashivli

Nielsen³

2006

Phys. Atom. Nuclei

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The multiple point principle, according to which several vacuum states with the same energy density exist, is put forward as a fine-tuning mechanism predicting the ratio between the fundamental and electroweak scales in the Standard Model (SM). It is shown that this ratio is exponentially huge: ∼ e 40 . Using renormalisation group equations for the SM, we obtain the effective potential in the 2-loop approximation and investigate the existence of its postulated second minimum at the fundamental scale. The investigation of the evolution of the top quark Yukawa coupling constant in the 2-loop approximation shows that, with initial values of the top Yukawa coupling in the interval h(M t ) = 0.95 ± 0.03 (here M t is the top quark pole mass), a second minimum of the SM effective potential can exist in the region φ min2 ≈ 10 16 − 10 22 GeV. A prediction is made of the existence of a new bound state of 6 top quarks and 6 anti-top quarks, formed due to Higgs boson exchanges between pairs of quarks/anti-quarks. This bound state is supposed to condense in a new phase of the SM vacuum. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The existence of three vacuum states (new, electroweak and fundamental) solves the hierarchy problem in the SM.

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Phase transition in gauge theories and multiple-point model

Cited by 9 publications

References 47 publications

Non-Local Game of Life in 2D Quasicrystals

Non-Local Game of Life in 2D Quasicrystals

Phase Transition in Gauge Theories, Monopoles and the Multiple Point Principle

The fundamental-electroweak scale hierarchy in the standard model

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