2D fuzzy Anti-de Sitter space from matrix models

Understand

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.