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- Title
Infinite-dimensional topological field theories from Hurwitz numbers.
- Authors
Mironov, Andrey; Morozov, Aleksey; Natanzon, Sergey
- Abstract
Classical Hurwitz numbers of a fixed degree together with Hurwitz numbers of seamed surfaces give rise to a Klein topological field theory (see [A. Alexeevski and S. Natanzon, The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces, Izv. Math. 72(4) (2008) 627-646]). We extend this construction to Hurwitz numbers of all degrees simultaneously. The corresponding infinite-dimensional Cardy-Frobenius algebra is computed in terms of Young diagrams and bipartite graphs. This algebra turns out to be isomorphic to the algebra of differential operators introduced in [A. Mironov, A. Morozov and S. Natanzon, Cardy-Frobenius extension of algebra of cut-and-join operators, J. Geom. Phys. 73 (2012) 243-251, arXiv:1210.6955; A Hurwitz theory avatar of open-closed string, Eur. Phys. J. C 73(2) (2013) 1-10, arXiv:1208.5057], which serves a model for open-closed string theory. We prove that the operators corresponding to Young diagrams and bipartite graphs give rise to relations between Hurwitz numbers.
- Subjects
TOPOLOGICAL fields; BIPARTITE graphs; HURWITZ polynomials; NUMBER theory; TOPOLOGICAL degree; PATHS &; cycles in graph theory; DIFFERENTIAL operators
- Publication
Journal of Knot Theory & Its Ramifications, 2014, Vol 23, Issue 6, p-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216514500333