Approximate treatment of noncommutative curvature in quartic matrix model

Abstract

We study a Hermitian matrix model with the standard quartic potential amended by a tr(RΦ2) term for fixed external matrix R. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model — a renormalizable noncommutative field theory. The extra term breaks the unitary symmetry of the action and leads, after perturbative calculation of the unitary integral, to an effective multitrace matrix model. Accompanying the analytical treatment of this multitrace approximation, we also study the model numerically by Monte Carlo simulations. The phase structure of the model is investigated, and a modified phase diagram is identified. We observe a shift of the transition line between the 1-cut and 2-cut phases of the theory that is consistent with the previous numerical simulations and also with the removal of the noncommutative phase in the Grosse-Wulkenhaar model.

Towards removal of striped phase in matrix model description of fuzzy field theories

“…We have analyzed the model also analytically in [5]. As the first step, we concentrate on the effect of the curvature term and discard the kinetic term…”

“…We give some necessary introductory information -about the fuzzy physics and its description in terms of the matrix models -in section 2. We then describe the results for the fate of the striped phase for the case of the fuzzy sphere from [4] in section 3 and results for the curvature part of the Grosse-Wulkenhaar model from [5] in section 4. We conclude with some outlook for future research.…”