Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations

A bstract Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized WDVV equations of [42]. We consider the Hurwitz p...

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Published in:The journal of high energy physics Vol. 2011; no. 11
Main Authors: Mironov, A., Morozov, A., Natanzon, S.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.11.2011
Springer Nature B.V
Subjects:
Chemical partition
Classical and Quantum Gravitation
Correlators
Elementary Particles
High energy physics
Mathematical analysis
Multiplication
Operators (mathematics)
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
Topology
Integrable Hierarchies
Topological Field Theories
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized WDVV equations of [42]. We consider the Hurwitz partition functions, associated in this way with the CAA of cut-and-join operators. The ordinary Hurwitz numbers for a given number of sheets in the covering provide trivial (sums of exponentials) solutions to the WDVV equations, with finite number of time-variables. The generalized Hurwitz numbers from [32, 33] provide a non-trivial solution with infinite number of times. The simplest solution of this type is associated with a subring, generated by the dilatation operators .
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP11(2011)097