Special Issue "Selected Papers: 10th Mathematical Physics Meeting"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics and Symmetry".

Deadline for manuscript submissions: closed (30 April 2020).

Special Issue Editor

Prof. Dr. Branko Dragovich
Website
Guest Editor
Institute of Physics, University of Belgrade, Serbia
Interests: theoretical and mathematical physics;, genetic code and bioinformation
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Special Issue Information

Dear Colleagues,

10th Mathematical Physics Meeting: School and Conference on Modern Mathematical Physics (http://mphys10.ipb.ac.rs/) is organized by the Institute of Physics, University of Belgrade, Serbia, and will be held in Belgrade, Serbia, 9–14 September 2019. This is a jubilee of the very successful  series of international school-conferences on modern mathematical physics organized and held in Serbia since 2001. Topics include various aspects of cosmology, gravity, quantum field theory, string theory, symmetries, nonperturbative approaches, integrable models, and mathematical methods. The proceedings of all previous meetings have been published by the Institute of Physics, Belgrade. This time, selected papers will be published in a Special Issue of the MDPI journal Symmetry, after peer review.

Prof. Dr. Branko Dragovich
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (9 papers)

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Research

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Open AccessArticle
Gas of Baby Universes in JT Gravity and Matrix Models
Symmetry 2020, 12(6), 975; https://doi.org/10.3390/sym12060975 - 08 Jun 2020
Abstract
It has been shown recently by Saad, Shenker and Stanford that the genus expansion of a certain matrix integral generates partition functions of Jackiw-Teitelboim (JT) quantum gravity on Riemann surfaces of arbitrary genus with any fixed number of boundaries. We use an extension [...] Read more.
It has been shown recently by Saad, Shenker and Stanford that the genus expansion of a certain matrix integral generates partition functions of Jackiw-Teitelboim (JT) quantum gravity on Riemann surfaces of arbitrary genus with any fixed number of boundaries. We use an extension of this integral for studying gas of baby universes or wormholes in JT gravity. To investigate the gas nonperturbatively we explore the generating functional of baby universes in the matrix model. The simple particular case when the matrix integral includes the exponential potential is discussed in some detail. We argue that there is a phase transition in the gas of baby universes. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
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Open AccessArticle
Some Cosmological Solutions of a New Nonlocal Gravity Model
Symmetry 2020, 12(6), 917; https://doi.org/10.3390/sym12060917 - 02 Jun 2020
Abstract
In this paper, we investigate a nonlocal modification of general relativity (GR) with action S = 1 16 π G [ R 2 Λ + ( R 4 Λ ) F ( ) ( R 4 Λ ) [...] Read more.
In this paper, we investigate a nonlocal modification of general relativity (GR) with action S = 1 16 π G [ R 2 Λ + ( R 4 Λ ) F ( ) ( R 4 Λ ) ] g d 4 x , where F ( ) = n = 1 + f n n is an analytic function of the d’Alembertian □. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if Λ 0 , k = 0 , and they have no analogs in Einstein’s gravity with cosmological constant Λ . One of these two solutions is a ( t ) = A t e Λ 4 t 2 , that mimics properties similar to an interference between the radiation and the dark energy. Another solution is a nonsingular bounce one a ( t ) = A e Λ t 2 . For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator F ( ) , which satisfies obtained necessary conditions. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
Open AccessArticle
Highly Entangled Spin Chains and 2D Quantum Gravity
Symmetry 2020, 12(6), 916; https://doi.org/10.3390/sym12060916 - 02 Jun 2020
Abstract
Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal novel features of quantum entanglement. [...] Read more.
Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal novel features of quantum entanglement. As a study of the systems from a different viewpoint, we introduce large-N matrix models with so-called A B A B interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams. Including loop diagrams naturally defines an extension of the Motzkin and Fredkin spin chains. Contribution from the whole loop effects at large N gives the growth of the power of 3 / 2 (with logarithmic correction), further beyond the square-root scaling. The loop contribution provides fluctuating two-dimensional bulk geometry, and the enhancement of the entanglement is understood as an effect of quantum gravity. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
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Open AccessArticle
Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
Symmetry 2020, 12(4), 620; https://doi.org/10.3390/sym12040620 - 14 Apr 2020
Abstract
The higher category theory can be employed to generalize the B F action to the so-called 3 B F action, by passing from the notion of a gauge group to the notion of a gauge 3-group. The theory of scalar electrodynamics coupled to [...] Read more.
The higher category theory can be employed to generalize the B F action to the so-called 3 B F action, by passing from the notion of a gauge group to the notion of a gauge 3-group. The theory of scalar electrodynamics coupled to Einstein–Cartan gravity can be formulated as a constrained 3 B F theory for a specific choice of the gauge 3-group. The complete Hamiltonian analysis of the 3 B F action for the choice of a Lie 3-group corresponding to scalar electrodynamics is performed. This analysis is the first step towards a canonical quantization of a 3 B F theory, an important stepping stone for the quantization of the complete scalar electrodynamics coupled to Einstein–Cartan gravity formulated as a 3 B F action with suitable simplicity constraints. It is shown that the resulting dynamic constraints eliminate all propagating degrees of freedom, i.e., the 3 B F theory for this choice of a 3-group is a topological field theory, as expected. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
Open AccessArticle
Dynamically Generated Inflationary ΛCDM
Symmetry 2020, 12(3), 481; https://doi.org/10.3390/sym12030481 - 20 Mar 2020
Cited by 1
Abstract
Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with [...] Read more.
Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden, nonlinear Noether symmetry which produces an energy-momentum tensor identified as the sum of a dynamically generated cosmological constant and dust-like dark matter. The non-Riemannian volume-element in the initial Einstein–Hilbert action upon passage to the physical Einstein-frame creates, dynamically, a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
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Open AccessArticle
Algebraic Bethe Ansatz for the Trigonometric sℓ(2) Gaudin Model with Triangular Boundary
Symmetry 2020, 12(3), 352; https://doi.org/10.3390/sym12030352 - 01 Mar 2020
Abstract
In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary [...] Read more.
In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
Open AccessArticle
Transverse Kähler–Ricci Solitons of Five-Dimensional Sasaki–Einstein Spaces Yp,q and T1,1
Symmetry 2020, 12(3), 330; https://doi.org/10.3390/sym12030330 - 25 Feb 2020
Abstract
We investigate the deformations of the Sasaki–Einstein structures of the five-dimensional spaces T 1 , 1 and Y p , q by exploiting the transverse structure of the Sasaki manifolds. We consider local deformations of the Sasaki structures preserving the Reeb vector fields [...] Read more.
We investigate the deformations of the Sasaki–Einstein structures of the five-dimensional spaces T 1 , 1 and Y p , q by exploiting the transverse structure of the Sasaki manifolds. We consider local deformations of the Sasaki structures preserving the Reeb vector fields but modify the contact forms. In this class of deformations, we analyze the transverse Kähler–Ricci flow equations. We produce some particular explicit solutions representing families of new Sasakian structures. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
Open AccessArticle
Disformal Transformations in Modified Teleparallel Gravity
Symmetry 2020, 12(1), 152; https://doi.org/10.3390/sym12010152 - 11 Jan 2020
Cited by 1
Abstract
In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion [...] Read more.
In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for f ( T ) gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz breaking terms that characterize it. However, we have shown that disformal transformations have interesting properties, which can be useful for future applications in scalar-torsion gravity models, among others. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)

Review

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Open AccessReview
Challenges in Supersymmetric Cosmology
Symmetry 2020, 12(3), 468; https://doi.org/10.3390/sym12030468 - 16 Mar 2020
Abstract
We discuss the possibility that inflation is driven by supersymmetry breaking with the scalar component of the goldstino superfield (sgoldstino) playing the role of the inflaton and charged under a gauged U ( 1 ) R-symmetry. Imposing a linear superpotential allows us to [...] Read more.
We discuss the possibility that inflation is driven by supersymmetry breaking with the scalar component of the goldstino superfield (sgoldstino) playing the role of the inflaton and charged under a gauged U ( 1 ) R-symmetry. Imposing a linear superpotential allows us to satisfy easily the slow-roll conditions, avoiding the so-called η -problem, and leads to an interesting class of small field inflation models, characterised by an inflationary plateau around the maximum of the scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum describing the present phase of the Universe. Inflation can be driven by either an F- or a D-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and in the simplest case predict a rather small tensor-to-scalar ratio of primordial perturbations. We propose a generalisation of Fayet-Iliopoulos model as a microscopic model leading to this class of inflation models at low energy. Full article
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
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