Covariant star product on semi-conformally flat noncommutative Calabi–Yau manifolds and noncommutative topological index theorem

DOI10.1142/s0219887823501682arXiv2112.04051OpenAlexW4362475469WikidataQ122525314 ScholiaQ122525314MaRDI QIDQ6184035

Amir Abbass Varshovi

Publication date: 24 January 2024

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.04051

zbMATH Keywords

Calabi-Yau manifoldKähler formsuperconnectionChern-Weil theorycovariant star productnoncommutative topological index theoremsemi-conformally flat metric

Mathematics Subject Classification ID

Differential geometry (53-XX) Relativity and gravitational theory (83-XX)

Cites Work

• The index theorem for topological manifolds
• Exact Seiberg-Witten map, induced gravity and topological invariants in non-commutative field theories
• Covariant non-commutative space-time
• A Levi-flat in a Kummer surface whose complement is strongly pseudoconvex
• Axiomatic quantum field theory in terms of operator product expansions: general framework, and perturbation theory via Hochschild cohomology
• Kähler flat manifolds
• Superconnections and the Chern character
• Topological quantum field theory
• Instanton invariants and flat connections on the Kummer surface
• The invariant theory of \(n\times n\) matrices
• Deformation theory and quantization. I: Deformations of symplectic structures
• Deformation theory and quantization. II: Physical applications
• A path integral approach to the Kontsevich quantization formula.
• String theory and noncommutative geometry
• Emergent gravity on covariant quantum spaces in the IKKT model
• An application of gauge theory to four dimensional topology
• Calabi-Yau manifolds and related geometries. Lectures at a summer school in Nordfjordeid, Norway, June 2001
• Deformation quantization of Poisson manifolds
• Topological methods in algebraic geometry. Translation from the German and appendix one by R. L. E. Schwarzenberger. Appendix two by A. Borel.
• Monopoles and four-manifolds
• Covariant star-products
• \(\star\)-cohomology, Connes-Chern characters, and anomalies in general translation-invariant noncommutative Yang-Mills
• Four-dimensional gravity on a covariant noncommutative space
• Noncommutative gravity solutions
• The index of elliptic operators. I
• The index of elliptic operators. III
• On Azumaya algebras and finite dimensional representations of rings
• Topological quantum field theory and four manifolds.
• THE SEIBERG–WITTEN MAP FOR NON-COMMUTATIVE PURE GRAVITY AND VACUUM MAXWELL THEORY
• Consistent anomalies in translation-invariant noncommutative gauge theories
• Differential Geometry
• Characteristic Classes and Homogeneous Spaces, I
• Dirac operators coupled to vector potentials
• ANOMALIES IN NONCOMMUTATIVE GAUGE THEORIES, SEIBERG–WITTEN TRANSFORMATION AND RAMOND–RAMOND COUPLINGS
• Diffeomorphism covariant star products and noncommutative gravity
• NONCOMMUTATIVE BLACK HOLES, THE FINAL APPEAL TO QUANTUM GRAVITY: A REVIEW
• Foundations of Hyperbolic Manifolds
• EXACT SEIBERG–WITTEN MAP AND INDUCED GRAVITY FROM NONCOMMUTATIVITY
• COVARIANT STAR PRODUCT ON SYMPLECTIC AND POISSON SPACE–TIME MANIFOLDS
• Characteristic Classes. (AM-76)
• TRACE IDENTITIES OF FULL MATRIX ALGEBRAS OVER A FIELD OF CHARACTERISTIC ZERO
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Covariant realization of quantum spaces as star products by Drinfeld twists
• Nonperturbative Topological Phenomena in QCD and Related Theories
• On the quantum structure of space-time, gravity, and higher spin in matrix models
• Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
• A gravity theory on noncommutative spaces
• Magnetic Monopoles
• The index of elliptic operators on compact manifolds
• On the principles of elementary quantum mechanics
• Noncommutative geometry and gravity
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