New recursive residue formulas for the topological expansion of the Cauchy Matrix Model

Details New recursive residue formulas for the topological expansion of the Cauchy Matrix Model New recursive residue formulas for the topological expansion of the Cauchy Matrix Model

2009-12-15

arxiv.org/abs/0912.2984v4

JHEP 1010:090,2010

Physics

Mathematical Physics

42 pages, one appendix added, referee comments added, minor typos corrected

Scientific paper

10.1007/JHEP10(2010)090

In a recent work [1] we consider the topological expansion for the non-mixed observables (including the free energy) for the formal Cauchy matrix model. The only restriction in [1] was the fact that all the branch points have to be simple. This excludes a very interesting situation not encountered in the literature before, namely the case in which two branch points merge in such a way that no cycle is pinched. In this work we focus on this situation and derive new formulas that apply to non-simple and non-singular branch-points.

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