Higher form gauge fields and their nonassociative symmetry algebras

Castellani, Leonardo

doi:10.1007/jhep09(2014)055

Cited by 11 publications

(21 citation statements)

References 26 publications

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“…This 3-cocycle provides the twisting of the pertinent horizontal product of the Lie 2-group, which was calculated explicitly for the case of toroidal backgrounds using the Baker-Campbell-Hausdorff formula. At the algebraic level, this 3-cocycle is exactly the one that appeared recently in [11], where R-space nonassociativity was similarly characterised in terms of 3-cocycles of the abelian group of translations in phase space with and without central extension using the deformation theory of Lie algebras (see also [22]).…”

Section: Introductionmentioning

confidence: 69%

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Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

Mylonas

Schupp

Szabo

2014

Journal of Mathematical Physics

189

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We analyse the symmetries underlying nonassociative deformations of geometry in nongeometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux. *

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Section: Introductionmentioning

confidence: 69%

“…22) respectively, where R IJK := ∂ K Θ IJ is constant and non-zero (and then equal to R ijk ) only for (selected) configuration space coordinates, c.f. (3.34) and (3.27).…”

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confidence: 99%

Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

Mylonas

Schupp

Szabo

2014

Journal of Mathematical Physics

189

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“…This non‐associative algebraic structure was further analyzed in refs. in terms of 3‐cocycles, star‐products, tri‐products and related physics topics such as membrane sigma‐models, magnetic monopole backgrounds, and their quantization.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…It was found that closed strings on non‐geometric flux backgrounds have surprising features in that they exhibit non‐commutativity and non‐associativity among the closed string coordinates and their momenta . These new algebraic structures were investigated further in a subsequent series of papers , focusing on the derivation of the commutation relations for different string models and their mathematical interpretation. Independent studies by other authors, following a more mathematical line of thought, have also come to the conclusion that non‐commutative and non‐associative tori arise from geometric flux vacua by a sequence of T‐dualities .…”

Section: Introductionmentioning

confidence: 99%

T‐duality, Quotients and Currents for Non‐Geometric Closed Strings

Bakas

Lüst

2015

Fortschritte der Physik

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We use the canonical description of T-duality as well as the formulation of T-duality in terms of chiral currents to investigate the geometric and non-geometric faces of closed string backgrounds originating from principal torus bundles with constant Hflux. Employing conformal field theory techniques, the non-commutative and nonassociative structures among generalized coordinates in the so called Q-flux and Rflux backgrounds emerge by gauging the Abelian symmetries of an enlarged Roček-Verlinde sigma-model and projecting the associated chiral currents of the enlarged theory to the T-dual coset models carrying non-geometric fluxes. *

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“…Previous studies have shown that spontaneous compactness of d = 11 supergravity results in the following Einstein equation solutions (in the form of Castellani and Warner [88]- [90] ):…”

Section: High-dim Supergravity and High-dim Superrepulsionmentioning

confidence: 99%

Cosmic Evolution Physics (I) for Supergravity and Dark-Energy with Super-Inflation

Li¹

2020

Preprint

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To solve a series of major problems, such as the singularity before the Big Bang, the inflation of the early universe and the accelerating expansion of the present universe, this series of studies start with super gravity, dark energy and dark matter, go beyond the surface of a lot of observation data, and systematically reveal the arche-internal mechanism of all things, to establish the arche-unity of physics, and give a natural and reasonable explanation. At present, there are at least three basic pathways that are leading our research field to repulsion against gravitation, quantum repulsion against quantum gravitation and high-dimensional superrepulsion against high-dimensional supergravity, that is, the research on the accelerating expansion mechanism of the current universe, the research on the dynamic mechanism of the early cosmic inflation, and the research on the rebound mechanism near the singularity before the Big Bang. In this series of studies, the arche problem of everything is always placed under the extreme environmental conditions of the initial universe, the starting point of scientific logic is closely combined with the starting point of the universe history, the pseudo vacuum energy considered by the inflationary universe model, the Higgs field predicted by the standard physical model and the dark energy speculated by the observational cosmology are reduced to the positive energy system with strong negative pressure, and they are reduced to the repulsion (all the resistance to gravity) that forms a conjugate relation with gravity. In our opinion, dark energy and dark matter are essentially at the level of quantum gravity and quantum repulsion. Therefore, we not only consider the conventional quantum effect and non commutative quantum effect, but also further consider the arche-conjugate effect and the cluster resonance-at-cofrenquence effect. For noncommutative space-time, we put forth the ultimate supersymmetry, the arche-conjugation and the cluster resonance-at-cofrenquence. A relatively complete natural mechanism forms such an important inference: the closer they get to Planck scale, the stronger the conventional quantum effect, non commutative quantum effect, arche-conjugate effect and co-frequency resonance effect are. In the high-dimensional space-time (the 11 dimensional hyperspace compactly reduced to M 4 × N r ), corresponding to the introduction of supergravity with the supersymmetry between the graviton and the gravitino, we put forth the superrepulsion with the supersymmetry between the repulsion and the repulsitino, and establish the arche-conjugate relationship between the high-dimensional supergravity and the high-dimensional superrepulsion. Therefrom, we propose a basic inference that can be promoted to the principle of hyperholography of high-dimensional universe (or multiuniverse): in a parallel universe formed by mutual coupling and holographic correspondence between the P universe dominated by negative pressure (high-dimensional superrepulsion and quantum repulsion of accumulating positive energy, mainly composed of dark energy) and the N universe dominated by positive pressure (high-dimensional supergravity and quantum gravity of accumulating negative energy, mainly composed of dark matter), there is a correspondence between the small-scale physics (ultraviolet cutoff) of the P universe and the large-scale physics (infrared cutoff) of the N universe, while there is a correspondence between the large-scale physics (ultraviolet cutoff) of the P universe and the small-scale physics (infrared cutoff) of the N universe. In the new research paradigms set in this series, the arche-conjugation between the high-dimensional supergravity and the high-dimensional super repulsion, as well as between the quantum gravity and the quantum repulsion, is higher than the supersymmetry, so it becomes the core concept of the new theory. The arhce-unity of physics is a super unity that transcends the grand unification of four basic interaction, which is formed between high-dimensional supergravity (related to dark matter) and high-dimensional superrepulsion (related to dark energy), between quantum gravity (related to dark matter) and quantum repulsion (related to dark energy). From the basic component point of view, before or after the big bang, the gravitons and repulsons are coupled together, the negative energy contraction dominated by the positive pressure and the positive energy expansion dominated by the negative pressure work alternately, forming the arche-conjugate pulsaton of neither the point particle nor the linear superstring. Under the big unified framework of quantum gravitational field and quantum repulsive field, this series of work comprehensively expands the general relativity and loop quantum ring gravitation theory, sets up the quantum repulsive field equation corresponding to the quantum gravitational field equation, and then establishes the quantum hedge-unified field equation describing the interaction of quantum gravitational field and quantum repulsive field; On this basis, the quantum repulsive universe equation corresponding to the quantum gravitational universe equation is established, thus a set of new equations describing the expansive universe with quantum hedge-unified field are established. On the one hand, scalar disturbance is considered as the exhibition of repulsive effect, on the other hand, tensor disturbance is considered as the exhibition of gravitational effect. In the initial stage of the big ripping, due to the mutual restraint of quantum repulsion and quantum gravity, the scalar and tensor perturbations are not obvious. However, at the end of the big ripping, the scalar and tensor perturbations are very significant, and there is a large power spectral exponential run. Between particle physics and cosmology, we improve and expand the path integral of quantum gravity, create the path integral of quantum hedge-unified field, and set up the basic equation of quantum cosmic-synergetic dynamics, and then establish the basic equation of quantum-cosmic paradigm dynamics. Thus we put up the operator distribution function and its dynamic equation of the quantum arche- pulsaton, and finally use the Wigner-Ville distribution as a non-linear time-frequency distribution to establish the Wigner joint-distribution of quantum-conjuagted pulsation function, so as to analyze the arche of all things with three evolutionary forms: quantum chaotic-pulsaton, quantum quasi-spherical pulsaton and quantum spherical-pulsaton. In this series of work, the mechanism to avoid the singularity of the universe is put forward fundamentally, and the dark energy and dark matter are explained through new mechanisms and effects at the level of quantum gravity. Between particle physics and cosmology, we improve and expand the path integral of quantum gravity, establish the path integral of quantum hedge-unified field, thus establish the basic equation of quantum cosmic-synergy dynamics, and then establish the basic equation of quantum cosmic-paradigm dynamics. Thus the covariant gravitational mass and the covariant inertial mass formed by the ultra-synergy between particles and the universe are presented, and the equivalence hypothesis on the covariant non-inertial system which can be elevated to the basic principle, is presented. Based on this hypothesis, a systematic calculation and analysis of binary stars composed of neutron stars and black holes are made. The master equation, variance and Fokker-Planck equation for the birth-death and migration of a large number of particles are established between binary stars composed of neutron stars and black holes.

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Higher form gauge fields and their nonassociative symmetry algebras

Cited by 11 publications

References 26 publications

Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

T‐duality, Quotients and Currents for Non‐Geometric Closed Strings

Cosmic Evolution Physics (I) for Supergravity and Dark-Energy with Super-Inflation

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