Multi-Matrix Models: Integrability Properties and Topological Content

Details Multi-Matrix Models: Integrability Properties and Topological Content Multi-Matrix Models: Integrability Properties and Topological Content

1995-06-19

arxiv.org/abs/hep-th/9506124v1

Int.J.Mod.Phys. A11 (1996) 1797-1830

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, Latex

Scientific paper

We analyze multi--matrix chain models. They can be considered as multi--component Toda lattice hierarchies subject to suitable coupling conditions. The extension of such models to include extra discrete states requires a weak form of integrability. The discrete states of the $q$--matrix model are organized in representations of $sl_q$. We solve exactly the Gaussian--type models, of which we compute several all-genus correlators. Among the latter models one can classify also the discretized $c=1$ string theory, which we revisit using Toda lattice hierarchy methods. Finally we analyze the topological field theory content of the $2q$--matrix models: we define primary fields (which are $\infty^q$), metrics and structure constants and prove that they satisfy the axioms of topological field theories. We outline a possible method to extract interesting topological field theories with a finite number of primaries.

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