Integrability of Hurwitz partition functions

被引：64

作者：

Alexandrov, A. ^{[1
,2
,3
]}

Mironov, A. ^{[3
,4
]}

Morozov, A. ^{[3
]}

Natanzon, S. ^{[3
,5
,6
]}

机构：

[1] LPTENS, Paris, France

[2] IPhT, Gif Sur Yvette, France

[3] ITEP, Moscow, Russia

[4] PN Lebedev Phys Inst, Moscow, Russia

[5] Higher Sch Econ, Dept Math, Moscow, Russia

[6] Moscow MV Lomonosov State Univ, AN Belozersky Inst, Moscow, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2012年 / 45卷 / 04期

关键词：

MATRIX MODELS; KONTSEVICH MODEL; EQUIVALENCE; EQUATIONS;

D O I：

10.1088/1751-8113/45/4/045209

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Partition functions often become tau-functions of integrable hierarchies, if they are considered dependent on infinite sets of parameters called time variables. The Hurwitz partition functions Z = Sigma(R) d(R)(2-k) chi R-R(t((1))) .... chi(R)(t((k)))exp(Sigma(n) xi C-n(R)(n))depend on two types of such time variables, t and xi. KP/Toda integrability in t requires that k <= 2 and also that C-R(n) are selected in a rather special way, in particular the naive cut-and-join operators are not allowed for n > 2. Integrability in. further restricts the choice of CR(n), forbidding, for example, the free cumulants. It also requires that k <= 1. The quasi-classical integrability (the WDVV equations) is naturally present in xi variables, but also requires a careful definition of the generating function.

引用

页数：10