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EnglishWe 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 slq. 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 ∞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.
| Titolo: | Multimatrix models: Integrability properties and topological content |
| Autori: | |
| Data di pubblicazione: | 1996 |
| Rivista: | |
| Abstract: | 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 slq. 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 ∞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. |
| Handle: | http://hdl.handle.net/11368/2900783 |
| Digital Object Identifier (DOI): | 10.1142/S0217751X9600095X |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |