Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The local Gromov-Witten theory of CP^1 and integrable hierarchies   In this paper we begin the study of the relationship between the local
Gromov-Witten theory of Calabi-Yau rank two bundles over the projective line
and the theory of integrable hierarchies. We first of all construct explicitly,
in a large number of cases, the Hamiltonian dispersionless hierarchies that
govern the full descendent genus zero theory. Our main tool is the application
of Dubrovin's formalism, based on associativity equations, to the known results
on the genus zero theory from local mirror symmetry and localization. The
hierarchies we find are apparently new, with the exception of the resolved
conifold O(-1) + O(-1) -> P1 in the equivariantly Calabi-Yau case. For this
example the relevant dispersionless system turns out to be related to the
long-wave limit of the Ablowitz-Ladik lattice. This identification provides us
with a complete procedure to reconstruct the dispersive hierarchy which should
conjecturally be related to the higher genus theory of the resolved conifold.
We give a complete proof of this conjecture for genus g<=1; our methods are
based on establishing, analogously to the case of KdV, a "quasi-triviality"
property for the Ablowitz-Ladik hierarchy at the leading order of the
dispersive expansion. We furthermore provide compelling evidence in favour of
the resolved conifold/Ablowitz-Ladik correspondence at higher genus by testing
it successfully in the primary sector for g=2.

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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th