Geometric Flow Equations for the Number of Space‐Time Dimensions

Biasio, Davide De; Julian, Freigang,; Lüst, Dieter

doi:10.1002/prop.202100171

Cited by 7 publications

(51 citation statements)

References 18 publications

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“…We omit such technical details in this work because they can be derived in abstract form following geometric principles and the Convention 2 (26). For recent applications in high energy physics, we cite [23,24,25,26,27] where the normalizing function is postulated as a dilaton field and associative and commutative versions of metric-dilaton Ricci flows are investigated. Certain geometric flow equations can be also motivated as star product R-flux deformations of a two-dimensional sigma model with beta functions and dilaton field (see equations ( 79) and (80) in [23]).…”

Section: A S-adapted Variational Procedures For Deriving Nonassociati...mentioning

confidence: 99%

“…The nonassociative geometric flow constructions provided in this section can be re-defined in terms of respective LC-connections, ⋆ ∇ and ∇, if we impose additional nonholonomic constraints of type (25), when…”

Section: Nonassociative Ricci Soliton Equations In Canonical S-variablesmentioning

confidence: 99%

“…In connection to this, we note the swampland program [19,20,21] which main goal is to elaborate rigorous criteria how to distinguish the low-energy effective field theories that can be completed in the UV from those that cannot. The swampland hypothesis in quantum gravity, QG, the infinite distance conjecture and various other someway related conjectures, were revisited recently in a series of works [22,23,24,25,26,27] using (non) commutative geometric flow, exact solutions in gravity theories, and quantum field methods. Here we emphasize that to elaborate on rigorous algebraic and geometric approaches to mathematical particle physics and QG, we have to consider models of nonassociative quantum mechanics, QM, [30,31] and further developments with nonassicative and noncommutative algebras [32,33,15,34,35,36].…”

mentioning

confidence: 99%

“…9 1.2 The structure, aims, and the main hypothesis of the paper This work is a natural and logical development of a series of articles on nonassociative geometry and physics [37,38,39] and a new research program on nonassociative geometric and quantum information flows and gravity [12,13,40,41]. It is related to the swampland program [19,20,21] and revised conjectures [23,24,25,26,27] following such five aims:…”

mentioning

confidence: 99%

“…In fact, for the AdS spaces, the Ricci flow swampland conjecture is equivalent to the anti-de Sitter distance conjecture (ADS) [20,23,24]. Swampland conjectures were studied recently in connection to BH physics, extra dimensions and geometric flow conjectures, when the concept of Bekenstein-Hawking entropy was applied [25,26,27]. A modern approach to QG and string and M-theory involves models with nonassocitative structures for QM, QFT and MGTs.…”

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confidence: 99%

See 4 more Smart Citations

Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

Bubuianu¹,

Vacaru

Veliev

2020

Annals of Physics

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Section: A S-adapted Variational Procedures For Deriving Nonassociati...mentioning

confidence: 99%

Section: Nonassociative Ricci Soliton Equations In Canonical S-variablesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

Bubuianu¹,

Vacaru

Veliev

2020

Annals of Physics

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Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

Bubuianu¹,

Vacaru

Veliev

2023

Fortschritte der Physik

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A theory of nonassociative geometric flows is formulated as an extension of a string‐inspired model of nonassociative gravity determined by star product. The nonassociative Ricci tensor and curvature scalar defined by (non) symmetric metric structures and generalized (non) linear connections are used for defining nonassociative versions of Grigori Perelman F‐ and W‐functionals for Ricci flows and computing associated thermodynamic variables. The anholonomic frame and connection deformation method, AFCDM, which allows us to construct exact and parametric solutions describing nonassociative geometric flow evolution scenarios and modified Ricci soliton configurations with quasi‐stationary generic off‐diagonal metrics are developed and applied. There are provided explicit examples of solutions modeling geometric and statistical thermodynamic evolution on a temperature‐like parameter of modified black hole configurations encoding nonassociative star‐product and R‐flux deformation data. Further perspectives of the paper are motivated by nonassociative off‐diagonal geometric flow extensions of the swampland program, related conjectures and claims on geometric and physical properties of new classes of quasi‐stationary Ricci flow and black hole solutions.

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Nonassociative Geometric and Quantum Information Flows and R‐Flux Deformations of Wormhole Solutions in String Gravity

Bubuianu,

Singleton,

Vacaru

et al. 2024

Fortschritte der Physik

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This article consists of an introduction to the theory of nonassociative geometric classical and quantum information flows defined by star products with R‐flux deformations in string gravity. Corresponding nonassociative generalizations of the concepts of classical Shannon entropy, quantum von Neumann entropy, Rényi entropy are formulated. The fundamental geometric and quantum information objects are computed following the Grigori Perelman statistical thermodynamic approach to Ricci flows and gravity theories generalized for phase spaces modeled as (co) tangent Lorentz bundles. Nonassociative parametric deformations and nonholonomic thermo‐geometric versions of statistical generating functions, their quantum analogues as density matrices are considered for deriving the entropy, energy and fluctuation functionals. This allows us to define and compute respective classical and quantum relative and conditional entropies, mutual information and nonassociative entanglement and thermodynamic information variables. The principles of nonassociative quantum geometric and information flow theory, QGIF, and study the basic properties of such quasi‐stationary models related to modified gravity theories are formulated. Applications are considered for nonassociative deformed and entangled couples of four‐dimensional (4‐d), wormholes (defined by respective spacetime and/or momentum type coordinates) and nonassociative QGIFs of 8‐d phase space generalized wormholes configurations. Finally, phase space black holes and wormholes being transversable for nonassociative qubits, quantum channels and entanglement witness are speculated; thought and laboratory experiments are discussed; and perspectives for quantum computer modeling and tests of nonassociative geometric flow and gravity theories are considered.

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Geometric Flow Equations for the Number of Space‐Time Dimensions

Cited by 7 publications

References 18 publications

Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

Nonassociative Geometric and Quantum Information Flows and R‐Flux Deformations of Wormhole Solutions in String Gravity

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