Kavli Affiliate: Todor E. Milanov
| First 5 Authors: Todor E. Milanov, , , ,
| Summary:
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.
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