Gromov--Witten Theory of CP^1 and Integrable Hierarchies

dc.creatorMilanov, Todor E.
dc.date2006-04-29
dc.date.accessioned2026-07-07T07:13:41Z
dc.date.available2026-07-07T07:13:41Z
dc.descriptionThe ancestor Gromov--Witten invariants of a compact {\Kahler} manifold $X$ can be organized in a generating function called the total ancestor potential of $X$. In this paper, we construct Hirota Quadratic Equations (HQE shortly) for the total ancestor potential of $\C P^1$. The idea is to adopt the formalism developed in \cite{G1,GM} to the mirror model of $\C P^1$. We hope that the ideas presented here can be generalized to other manifolds as well. As a corollary, using the twisted loop group formalism from \cite{G3}, we obtain a new proof of the following version of the Toda conjecture: the total descendant potential of $\C P^1$ (known also as the partition function of the $\C P^1$ topological sigma model) is a tau-function of the Extended Toda Hierarchy.
dc.description22 pages, this is the second part of an earlier version, major revision of the exposition
dc.identifierhttps://arxiv.org/abs/math-ph/0605001
dc.identifierhttp://arxiv.org/abs/math-ph/0605001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112565
dc.subjectMathematical Physics
dc.subject34S30
dc.titleGromov--Witten Theory of CP^1 and Integrable Hierarchies
dc.typetext

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