Towards Gauge theory for a class of commutative and non-associative fuzzy spaces

Abstract

We discuss gauge theories for commutative but non-associative algebras related to the $SO(2k+1)$ covariant finite dimensional fuzzy $2k$-sphere algebras. A consequence of non-associativity is that gauge fields and gauge parameters have to be generalized to be functions of coordinates as well as derivatives. The usual gauge fields depending on coordinates only are recovered after a partial gauge fixing.The deformation parameter for these commutative but non-associative algebras is a scalar of the rotation group. This suggests interesting string-inspired algebraic deformations of spacetime which preserve Lorentz-invariance.

arXiv comment34 pages ; v2, v3- minor typos fixed

References in corpus (26)

• String Theory and Noncommutative Geometry
• M Theory As A Matrix Model: A Conjecture
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• A Large-N Reduced Model as Superstring
• A Four Dimensional Generalization of the Quantum Hall Effect
• Noncommutative Yang-Mills in IIB Matrix Model
• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Noncommutative Spacetime, Stringy Spacetime Uncertainty Principle, and Density Fluctuations
• Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds
• A Note on Background Independence in Noncommutative Gauge Theories, Matrix Model and Tachyon Condensation
• On Finite 4D Quantum Field Theory in Non-Commutative Geometry
• On spherical harmonics for fuzzy spheres in diverse dimensions
• Coherent State Induced Star-Product on $R_{\lambda }^3$ and the Fuzzy Sphere
• Branes, Fluxes and Duality in M(atrix)-Theory
• Non-abelian Brane Intersections
• Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
• Longitudinal 5-branes as 4-spheres in Matrix theory
• Effective field theory description of the higher dimensional quantum Hall liquid
• Noncommutative geometry of angular momentum space U(su(2))
• Higher Dimensional Geometries from Matrix Brane constructions
• Non commutative gravity from the ADS/CFT correspondence
• Massive IIA String Theory and Matrix Theory Compactification
• Field Theory on the q-deformed Fuzzy Sphere II: Quantization
• Matrix Theory, AdS/CFT and Higgs-Coulomb Equivalence
• Non-Abelian BIonic Brane Intersections

Cited by in corpus (5)

• Fluctuating Fuzzy Funnels
• Matrix theory compactifications on twisted tori
• Tensor models and 3-ary algebras
• Colorless operators in a non-associative quantum theory
• A New Lorentz Violating Nonlocal Field Theory From String-Theory