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

Naoki Sasakura
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Abstract

A dynamical fuzzy space might be described in terms of a dynamical three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c of the functions f_a on a fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. The solutions to the invariant equations of motion of C_{ab}^c can be generally constructed from the invariant tensors of Lie groups. Euclidean models the actions of which are bounded from below are introduced. Lie group symmetric solutions to a class of Euclidean model are obtained. The analysis of the fluctuations around the SO(3) symmetric solution shows that the solution can be regarded as a fuzzy S^2/Z_2.

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Naoki Sasakura. 2005-12-07. An invariant approach to dynamical fuzzy spaces with a three-index variable -- Euclidean models. https://arxiv.org/abs/hep-th/0511154

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