English

An invariant approach to dynamical fuzzy spaces with a three-index variable

High Energy Physics - Theory 2009-11-11 v2 General Relativity and Quantum Cosmology

Abstract

A dynamical fuzzy space might be described by a three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c among the functions f_a on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. I study equations for the three-index variable invariant under the general linear transformation, and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, I study SO(3) symmetric solutions, and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework.

Keywords

Cite

@article{arxiv.hep-th/0506192,
  title  = {An invariant approach to dynamical fuzzy spaces with a three-index variable},
  author = {Naoki Sasakura},
  journal= {arXiv preprint arXiv:hep-th/0506192},
  year   = {2009}
}

Comments

Typos corrected, 12 pages, 8 figures, LaTeX, JHEP class

R2 v1 2026-07-22T15:30:41.077Z