Polynomial averages in the Kontsevich model

Details Polynomial averages in the Kontsevich model Polynomial averages in the Kontsevich model

1992-06-24

arxiv.org/abs/hep-th/9206090v1

Commun.Math.Phys. 151 (1993) 193-219

Physics

High Energy Physics

High Energy Physics - Theory

30 pages

Scientific paper

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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