L. Bonora et al., MULTIMATRIX MODELS - INTEGRABILITY PROPERTIES AND TOPOLOGICAL CONTENT, International journal of modern physics A, 11(10), 1996, pp. 1797-1830
In this article, we analyze multimatrix chain models. They can be cons
idered as multi-component Toda lattice hierarchies subject to suitable
coupling conditions. The extension of such models to include extra di
screte states requires a weak form of integrability. The discrete stat
es of the q-matrix model are organized in representations of sl(q). We
solve exactly the Gaussian type models, of which we compute several a
ll-genus correlators. Among the latter models one can classify also th
e discretized c = 1 string theory, which we revisit using Toda lattice
hierarchy methods. Finally, we analyze the topological field theory c
ontent of the 2q-matrix models: we define primary fields (which are co
(q))1 metrics and structure constants. and prove that they satisfy the
axioms of topological field theories. We outline a possible method fo
r extracting interesting topological field theories with a finite numb
er of primaries.