  The Gaussian Hermitian matrix model was recently proposed to have a dual
string description with worldsheets mapping to a sphere target space. The
correlators were written as sums over holomorphic (Belyi) maps from worldsheets
to the two-dimensional sphere, branched over three points. We express the
matrix model correlators by using the fuzzy sphere construction of matrix
algebras, which can be interpreted as a string field theory description of the
Belyi strings. This gives the correlators in terms of trivalent ribbon graphs
that represent the couplings of irreducible representations of su(2), which can
be evaluated in terms of 3j and 6j symbols. The Gaussian model perturbed by a
cubic potential is then recognised as a generating function for Ponzano-Regge
partition functions for 3-manifolds having the worldsheet as boundary, and
equipped with boundary data determined by the ribbon graphs. This can be viewed
as a holographic extension of the Belyi string worldsheets to membrane
worldvolumes, forming part of a holographic hierarchy linking, via the large N
expansion, the zero-dimensional QFT of the Matrix model to 2D strings and 3D
membranes.
