• Corpus ID: 237266516

KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions

@inproceedings{Alexandrov2021KPIO,
  title={KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions},
  author={Alexander Alexandrov},
  year={2021}
}
In this paper, we continue our investigation of the triple Hodge integrals satisfying the Calabi–Yau condition. For the tau-functions, which generate these integrals, we derive the complete families of the Heisenberg–Virasoro constraints. We also construct several equivalent versions of the cut-and-join operators. These operators describe the algebraic version of topological recursion. For the specific values of parameters associated with the KdV reduction, we prove that these tau-functions are… 
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References

SHOWING 1-10 OF 78 REFERENCES
Cut-and-join description of generalized Brezin-Gross-Witten model
We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we
Topological recursion on the Bessel curve
The Witten-Kontsevich theorem states that a certain generating function for intersection numbers on the moduli space of stable curves is a tau-function for the KdV integrable hierarchy. This
KP hierarchy for Hodge integrals
Abstract Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and
Hodge integrals and Gromov-Witten theory
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these
Enumerative Geometry, Tau-Functions and Heisenberg–Virasoro Algebra
In this paper we establish relations between three enumerative geometry tau-functions, namely the Kontsevich–Witten, Hurwitz and Hodge tau-functions. The relations allow us to describe the
The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers
Author(s): Eynard, Bertrand; Mulase, Motohico; Safnuk, Brad | Abstract: We calculate the Laplace transform of the cut-and-join equation of Goulden, Jackson and Vakil. The result is a polynomial
Open intersection numbers and free fields
Abstract A complete set of the Virasoro and W-constraints for the Kontsevich–Penner model, which conjecturally describes intersections on moduli spaces of open curves, was derived in our previous
KP hierarchy for Hurwitz-type cohomological field theories
Abstract. We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting
Virasoro constraints and polynomial recursion for the linear Hodge integrals
The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge
Hurwitz numbers, matrix models and enumerative geometry
We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric
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