Gromov--Witten Theory of CP^1 and Integrable Hierarchies
| dc.creator | Milanov, Todor E. | |
| dc.date | 2006-04-29 | |
| dc.date.accessioned | 2026-07-07T07:13:41Z | |
| dc.date.available | 2026-07-07T07:13:41Z | |
| dc.description | The 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.description | 22 pages, this is the second part of an earlier version, major revision of the exposition | |
| dc.identifier | https://arxiv.org/abs/math-ph/0605001 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0605001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112565 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 34S30 | |
| dc.title | Gromov--Witten Theory of CP^1 and Integrable Hierarchies | |
| dc.type | text |