$N=1$ formal genus $0$ Gromov-Witten theories and Givental's formalism

Details $N=1$ formal genus $0$ Gromov-Witten theories and Givental's formalism $N=1$ formal genus $0$ Gromov-Witten theories and Givental's formalism

2008-03-25

arxiv.org/abs/0803.3554v1

J.Geom.Phys.59:1127-1136,2009

Mathematics

Quantum Algebra

15 pages

Scientific paper

10.1016/j.geomphys.2009.04.014

In [Gi3] Givental introduced and studied a space of formal genus zero Gromov-Witten theories $GW_0$, i.e. functions satisfying string and dilaton equations and topological recursion relations. A central role in the theory plays the geometry of certain Lagrangian cones and a twisted symplectic group of hidden symmetries. In this note we show that the Lagrangian cones description of the action of this group coincides with the genus zero part of Givental's quantum Hamiltonian formalism. As an application we identify explicitly the space of $N=1$ formal genus zero GW theories with lower-triangular twisted symplectic group modulo the string flow.

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