Introduces cap amplitude ψ(b) in one-matrix models and interprets the dilaton equation for discrete volumes N_{g,n} as boundary gluing that reduces n by one.
Matrix models as conformal field theories: genus expansion
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abstract
We obtain the topological expansion of the hermitian matrix model using its representation as a CFT on a hyperelliptic Riemann surface. To each branch point of the Riemann surface we associate an operator which represents a twist field dressed by the modes of the twisted boson. The partition function of the matrix model is computed as a correlation function of such dressed twist fields. The perturbative construction of the dressing operators yields a set of Feynman rules for evaluating the free energy and the loop observables at any genus.
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Cap amplitudes in random matrix models
Introduces cap amplitude ψ(b) in one-matrix models and interprets the dilaton equation for discrete volumes N_{g,n} as boundary gluing that reduces n by one.