Proof of a conjecture on the genus two free energy associated to the An singularity

被引：4

作者：

Fu, Yulong ^{[1
]}

Liu, Si-Qi ^{[1
]}

Zhang, Youjin ^{[1
]}

Zhou, Chunhui ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2014年 / 76卷

关键词：

Frobenius manifold; G-function; Simple singularities; Dual graph; Free energy; TOPOLOGICAL FIELD-THEORY;

D O I：

10.1016/j.geomphys.2013.10.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a recent paper Dubrovin et al. (1998), it is proved that the genus two free energy of an arbitrary semisimple Frobenius manifold can be represented as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so called genus two G-function, and for a certain class of Frobenius manifolds it is conjectured that the associated genus two G-functions vanish. In this paper, we prove this conjecture for the Frobenius manifolds associated with simple singularities of type A. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：10 / 24

页数：15

共 23 条

[1] MEAN FIELD-THEORY, TOPOLOGICAL FIELD-THEORY, AND MULTIMATRIX MODELS [J].

DIJKGRAAF, R ;

WITTEN, E .

NUCLEAR PHYSICS B, 1990, 342 (03) :486-522

[2]

DIJKGRAAF R, 1992, NATO ADV SCI INST SE, V295, P95

[3]

DIJKGRAAF R, 1991, STRING THEORY AND QUANTUM GRAVITY, P91

[4] Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation [J].

Dubrovin, B ;

Zhang, YJ .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 198 (02) :311-361

[5] Extended affine Weyl groups and Frobenius manifolds [J].

Dubrovin, B ;

Zhang, YJ .

COMPOSITIO MATHEMATICA, 1998, 111 (02) :167-219

[6]

DUBROVIN B., 1996, Montecatini Terme, 1993), Lecture Notes in Math., V1620, P120, DOI 10.1007/BFb0094793

[7]

DUBROVIN B., ARXIVMATH0108160

[8] On the genus two free energies for semisimple Frobenius manifolds [J].

Dubrovin, Boris ;

Liu, Si-Qi ;

Zhang, Youjin .

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2012, 19 (03) :273-298

[9]

Faber C, 2010, ANN SCI ECOLE NORM S, V43, P621

[10]

Fan H., 1995, COMMUN PUR APPL MATH, V61, P745

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