2D fuzzy Anti-de Sitter space from matrix models

TL;DR

This paper explores fuzzy AdS^2 and dS^2 spaces as brane solutions in matrix models, demonstrating how matter induces gravitational perturbations and illustrating emergent gravity mechanisms.

Contribution

It provides explicit constructions of fuzzy hyperboloids in matrix models and shows how matter influences brane geometry, leading to emergent gravity phenomena.

Findings

Explicit formulas for fuzzy hyperboloids in matrix models.

Matter induces transversal brane perturbations.

Emergent gravity described by linearized Henneaux-Teitelboim theory.

Abstract

We study the fuzzy hyperboloids AdS^2 and dS^2 as brane solutions in matrix models. The unitary representations of SO(2,1) required for quantum field theory are identified, and explicit formulae for their realization in terms of fuzzy wavefunctions are given. In a second part, we study the (A)dS^2 brane geometry and its dynamics, as governed by a suitable matrix model. In particular, we show that trace of the energy-momentum tensor of matter induces transversal perturbations of the brane and of the Ricci scalar. This leads to a linearized form of Henneaux-Teitelboim-type gravity, illustrating the mechanism of emergent gravity in matrix models.