Polynomial averages in the Kontsevich model
High Energy Physics - Theory
2015-06-26 v1 Quantum Algebra
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.
Cite
@article{arxiv.hep-th/9206090,
title = {Polynomial averages in the Kontsevich model},
author = {P. Di Francesco and C. Itzykson and J. -B. Zuber},
journal= {arXiv preprint arXiv:hep-th/9206090},
year = {2015}
}
Comments
30 pages