English

The Harer--Zagier recursion for an irregular spectral curve

Mathematical Physics 2016-11-21 v2 High Energy Physics - Theory Geometric Topology math.MP

Abstract

We derive the Do and Norbury recursion formula for the one-loop mean of an irregular spectral curve from a variant of replica method by Brez\'in and Hikami. We express this recursion in special times in which all terms W1(g)W_1^{(g)} of the genus expansion of the one-loop mean are polynomials. We find a generalization of this recursion to the generalized Laguerre polynomial case.

Keywords

Cite

@article{arxiv.1512.09278,
  title  = {The Harer--Zagier recursion for an irregular spectral curve},
  author = {Leonid O. Chekhov},
  journal= {arXiv preprint arXiv:1512.09278},
  year   = {2016}
}

Comments

16 pages, no figures, presentation reshuffled, typos corrected, examples added