Nonassociative geometry of nonholonomic phase spaces with star R-flux string deformations and (non) symmetric metrics

Abstract

We elaborate on nonassociative differential geometry of phase spaces endowed with nonholonomic (non-integrable) distributions and frames, nonlinear and linear connections, symmetric and nonsymmetric metrics, and correspondingly adapted quasi-Hopf algebra structures. The approach is based on the concept of nonassociative star product introduced for describing closed strings moving in a constant R-flux background. Generalized Moyal-Weyl deformations are considered when, for nonassociative and noncommutative terms of star deformations, there are used nonholonomic frames (bases) instead of local partial derivatives. In such modified nonassociative and nonholonomic spacetimes and associated complex/ real phase spaces, the coefficients of geometric and physical objects depend both on base spacetime coordinates and conventional (co) fiber velocity/ momentum variables like in (non) commutative Finsler-Lagrange-Hamilton geometry. For nonassociative and (non) commutative phase spaces modelled as total spaces of (co) tangent bundles on Lorentz manifolds enabled with star products and nonholonomic frames, we consider associated nonlinear connection, N-connection, structures determining conventional horizontal and (co) vertical (for instance, 4+4) splitting of dimensions and N-adapted decompositions of fundamental geometric objects. There are defined and computed in abstract geometric and N-adapted coefficient forms the torsion, curvature and Ricci tensors. We extend certain methods of nonholonomic geometry in order to construct R-flux deformations of vacuum Einstein equations for the case of N-adapted linear connections and symmetric and nonsymmetric metric structures.

arXiv commentlatex2e, 69 pages, v2 with small typos corrections and updated reference comparing to v1, v3 is equivalent to the published version

References in corpus (47)

• Noncommutative Geometry and Gravity
• Noncommutative Quantum Gravity
• T-duality and closed string non-commutative (doubled) geometry
• Nonassociative Gravity in String Theory?
• Nonassociative tori and applications to T-duality
• Comments on noncommutative gravity
• Nonsymmetric Gravitational Theory
• Nonsymmetric Gravity Theories: Inconsistencies and a Cure
• Exact Solutions with Noncommutative Symmetries in Einstein and Gauge Gravity
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Noncommutative Gravity Solutions
• Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Non-associative Deformations of Geometry in Double Field Theory
• Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows
• Superstrings in Higher Order Extensions of Finsler Superspaces
• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• Gauge and Einstein Gravity from Non-Abelian Gauge Models on Noncommutative Spaces
• Locally Anisotropic Gravity and Strings
• Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
• Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
• Einstein Gravity as a Nonholonomic Almost Kahler Geometry, Lagrange-Finsler Variables, and Deformation Quantization
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
• Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics
• Nonassociative differential geometry and gravity with non-geometric fluxes
• Triproducts, nonassociative star products and geometry of R-flux string compactifications
• Instabilities in the nonsymmetric theory of gravitation
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Non-commutative deformation of Chern-Simons theory
• The cosmology of the nonsymmetric theory of gravitation
• Deforming Black Hole and Cosmological Solutions by Quasiperiodic and/or Pattern Forming Structures in Modified and Einstein Gravity
• Problems and hopes in nonsymmetric gravity
• Massive NGT and Spherically Symmetric Systems
• Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
• Linearisation Instabilities of the Massive Nonsymmetric Gravitational Theory
• Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems
• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• $L_{\infty }$-Bootstrap Approach to Non-Commutative Gauge Theories
• Intersecting Branes, SUSY Breaking and the 2TeV Excess at the LHC
• Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
• Classical and quantum geometric information flows and entanglement of relativistic mechanical systems
• Weak associativity and deformation quantization
• Vacuum properties of nonsymmetric gravity in de Sitter space
• Dynamical Constraints in the Nonsymmetric Gravitational Theory

Cited by in corpus (6)

• Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity
• Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics
• Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures
• Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks
• Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories