Polynomial averages in the Kontsevich model |
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Authors: | P Di Francesco C Itzykson J B Zuber |
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Institution: | (1) Service de Physique Théorique de Saclay, Laboratoire de la Direction des Sciences et de la Matière du Commissariat à l'Energie Atomique, F-91191 Gif sur Yvette Cedex, France |
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Abstract: | We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic potential) measure, as derivatives of the partition function with respect to traces of inverse odd powers of the external argument. The proofs are based on elementary algebraic identities involving a new set of invariant polynomials of the linear group, closely related to the general Schur functions. |
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