New scheme for color confinement and violation of the non-Abelian Bianchi identities

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

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On supersymmetric AdS4 orientifold vacua

Journal of High Energy Physics ◽

10.1007/jhep08(2020)087 ◽

2020 ◽

Vol 2020 (8) ◽

Cited By ~ 1

Author(s):

Fernando Marchesano ◽

Eran Palti ◽

Joan Quirant ◽

Alessandro Tomasiello

Keyword(s):

String Theory ◽

Cosmological Constant ◽

Bianchi Identities ◽

Expansion Parameter ◽

First Order ◽

Ricci Flat ◽

Key Features ◽

One To One ◽

Calabi Yau Manifolds

Abstract In this work we study ten-dimensional solutions to type IIA string theory of the form AdS4 × X6 which contain orientifold planes and preserve $$ \mathcal{N} $$ N = 1 supersymmetry. In particular, we consider solutions which exhibit some key features of the four-dimensional DGKT proposal for compactifications on Calabi-Yau manifolds with fluxes, and in this sense may be considered their ten-dimensional uplifts. We focus on the supersymmetry equations and Bianchi identities, and find solutions to these that are valid at the two-derivative level and at first order in an expansion parameter which is related to the AdS cosmological constant. This family of solutions is such that the background metric is deformed from the Ricci-flat one to one exhibiting SU(3) × SU(3)-structure, and dilaton gradients and warp factors are induced.

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Dark matter, dark energy and gravity

International Journal of Modern Physics E ◽

10.1142/s0218301315500123 ◽

2015 ◽

Vol 24 (02) ◽

pp. 1550012 ◽

Cited By ~ 2

Author(s):

B. A. Robson

Keyword(s):

Dark Matter ◽

Dark Energy ◽

Particle Physics ◽

Composite Structures ◽

Gravitational Interaction ◽

Asymptotic Freedom ◽

Generation Model ◽

Newtonian Gravitation ◽

Color Confinement ◽

Vector Bosons

Within the framework of the Generation Model (GM) of particle physics, gravity is identified with the very weak, universal and attractive residual color interactions acting between the colorless particles of ordinary matter (electrons, neutrons and protons), which are composite structures. This gravitational interaction is mediated by massless vector bosons (hypergluons), which self-interact so that the interaction has two additional features not present in Newtonian gravitation: (i) asymptotic freedom and (ii) color confinement. These two additional properties of the gravitational interaction negate the need for the notions of both dark matter and dark energy.

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GEOMETRICAL CONSTRAINTS FOR D = 10, N = 1 SUPERGRAVITY

International Journal of Modern Physics A ◽

10.1142/s0217751x89001540 ◽

1989 ◽

Vol 04 (15) ◽

pp. 3819-3831 ◽

Cited By ~ 4

Author(s):

LING-LIE CHAU ◽

CHONG-SA LIM

Keyword(s):

Equations Of Motion ◽

Bianchi Identities ◽

Dynamical Consequence ◽

Integrability Conditions ◽

Geometrical Constraints ◽

Additional Constraints

A set of geometrical constraints for D = 10, N = 1 supergravity is formulated. It has the meaning as integrability conditions on "hyperplanes" determined by light-like lines in the superspace. The dynamical consequence of these geometrical constraints is studied via Bianchi identities. Since no equations of motion have resulted, these geometrical constraints can form an off-shell set of constraints for the theory. We also discuss additional constraints that lead to Poincare supergravity equations of motion. The relation of the theory with D = 4 N = 4 supergravity is also illuminated.

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ANOMALY FREE SUPERGRAVITY IN D=10: I) THE BIANCHI IDENTITIES AND THE BOSONIC LAGRANGIAN

International Journal of Modern Physics A ◽

10.1142/s0217751x88000436 ◽

1988 ◽

Vol 03 (04) ◽

pp. 953-1021 ◽

Cited By ~ 31

Author(s):

RICCARDO D’AURIA ◽

PIETRO FRÉ ◽

MARIO RACITI ◽

FRANCO RIVA

Keyword(s):

Differential Equation ◽

Boundary Conditions ◽

Variational Equation ◽

Second Order ◽

Effective Theory ◽

Spin Connection ◽

Bianchi Identities ◽

First Order ◽

Interaction Terms ◽

Starting Point

Using a theorem by Bonora-Pasti and Tonin on the existence of a solution for D=10N=1 Bianchi identities in the presence of a Lorentz Chern Simons term, we find an explicit parametrization of the superspace curvatures. Our solution depends only on one free parameter which can be reabsorbed in a field redefinition of the dilaton and of the gravitello. We emphasize that the essential point which enables us to obtain a closed form for the curvature parametrizations and hence for the supersymmetry transformation rules is the use of first order formalism. The spin connection is known once the torsion is known. This latter, rather than being identified with Hµνρ as it is usually done in the literature, is related to it by a differential equation which reduces to the algebraic relation Hµνρ = - 3Tµνρ e4/3σ only at γ1=0 (γ1 being proportional to κ/g2). The solution of the Bianchi identities exhibited in this paper corresponds to a D=10 anomaly free supergravity (AFS). This theory is unique in first order formalism but corresponds to various theories in second order formalism. Indeed the torsion equation is a differential equation which, in order to be solved must be supplemented with boundary conditions. One wonders whether supplemented with a judicious choice of boundary conditions for the torsion equation, AFS yields all the interaction terms found in the effective theory of the heterotic string (ETHS). In this respect two remarks are in order. Firstly it appears that solving the torsion equation iteratively with Tµνρ = -1/3Hµνρ e-4/3σ as starting point all the terms of ETHS except those with a ζ(3) coefficient show up. (Whether the coefficient agree is still to be checked.) Secondly, as shown in this paper the rheonomic solution of the super Poincaré Bianchi identities is unique. Hence additional interaction terms can be added to the Lagrangian only by modifying the rheonomic parametrization of the [Formula: see text]-curvature. The only assumption made in our paper is that [Formula: see text] has at most ψ∧ψ∧V components (sector (1,2)). Correspondingly the only room left for a modification of the present theory is the addition of a (0, 3) part in the rheonomic parametrization of [Formula: see text]. When this work was already finished a conjecture was published by Lechner Pasti and Tonin that such a generalization of AFS might exist and be responsible for the ζ(3) missing term. Indeed if we were able to solve the [Formula: see text]-Bianchi with this new (0, 3)-part then the torsion equation would be modified via new terms which, in second order formalism, lead to additional gravitational interactions. The equation of motion of Anomaly Free Supergravity can be worked out from the Bianchi identities: we indicate through which steps. The corresponding Lagrangian could be constructed with the standard procedures of the rheonomy approach. In this paper we limit ourselves to the bosonic sector of such a Lagrangian and we show that it can indeed be constructed in such a way as to produce the relation between Hµνρ and Tµνρ as a variational equation.

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