An invariant approach to dynamical fuzzy spaces with a three-index variable
arXiv:hep-th/0506192 · doi:10.1142/S0217732306020329
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.
Typos corrected, 12 pages, 8 figures, LaTeX, JHEP class