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17 pages, 1141 KiB

Open AccessArticle

Gas of Baby Universes in JT Gravity and Matrix Models

by Irina Aref’eva and Igor Volovich

Symmetry 2020, 12(6), 975; https://doi.org/10.3390/sym12060975 - 08 Jun 2020

Cited by 11 | Viewed by 1971

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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10 pages, 258 KiB

Open AccessArticle

Some Cosmological Solutions of a New Nonlocal Gravity Model

by Ivan Dimitrijevic, Branko Dragovich, Alexey S. Koshelev, Zoran Rakic and Jelena Stankovic

Symmetry 2020, 12(6), 917; https://doi.org/10.3390/sym12060917 - 02 Jun 2020

Cited by 11 | Viewed by 1619

Abstract

In this paper, we investigate a nonlocal modification of general relativity (GR) with action [...] Read more.

In this paper, we investigate a nonlocal modification of general relativity (GR) with action

S = \frac{1}{16 π G} \int [R - 2 Λ + (R - 4 Λ) F (□) (R - 4 Λ)] \sqrt{- g} d^{4} x,

where

F (□) = \sum_{n = 1}^{+ \infty} 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 \neq 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 \sqrt{t} e^{\frac{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)

23 pages, 327 KiB

Open AccessArticle

Highly Entangled Spin Chains and 2D Quantum Gravity

by Fumihiko Sugino

Symmetry 2020, 12(6), 916; https://doi.org/10.3390/sym12060916 - 02 Jun 2020

Cited by 2 | Viewed by 1874

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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21 pages, 385 KiB

Open AccessArticle

Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory

by Tijana Radenković and Marko Vojinović

Symmetry 2020, 12(4), 620; https://doi.org/10.3390/sym12040620 - 14 Apr 2020

Cited by 9 | Viewed by 1590

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)

22 pages, 1504 KiB

Open AccessArticle

Dynamically Generated Inflationary ΛCDM

by David Benisty, Eduardo I. Guendelman, Emil Nissimov and Svetlana Pacheva

Symmetry 2020, 12(3), 481; https://doi.org/10.3390/sym12030481 - 20 Mar 2020

Cited by 13 | Viewed by 3244

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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20 pages, 365 KiB

Open AccessArticle

Algebraic Bethe Ansatz for the Trigonometric sℓ(2) Gaudin Model with Triangular Boundary

by Nenad Manojlović and Igor Salom

Symmetry 2020, 12(3), 352; https://doi.org/10.3390/sym12030352 - 01 Mar 2020

Cited by 6 | Viewed by 2324

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)

11 pages, 284 KiB

Open AccessArticle

Transverse Kähler–Ricci Solitons of Five-Dimensional Sasaki–Einstein Spaces Y^p,q and T^1,1

by Mihai Visinescu

Symmetry 2020, 12(3), 330; https://doi.org/10.3390/sym12030330 - 25 Feb 2020

Cited by 2 | Viewed by 1514

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)

12 pages, 304 KiB

Open AccessArticle

Disformal Transformations in Modified Teleparallel Gravity

by Alexey Golovnev and María José Guzmán

Symmetry 2020, 12(1), 152; https://doi.org/10.3390/sym12010152 - 11 Jan 2020

Cited by 12 | Viewed by 1938

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

Jump to: Research

22 pages, 913 KiB

Open AccessReview

Challenges in Supersymmetric Cosmology

by Ignatios Antoniadis and Auttakit Chatrabhuti

Symmetry 2020, 12(3), 468; https://doi.org/10.3390/sym12030468 - 16 Mar 2020

Cited by 1 | Viewed by 1813

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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