Quantum Witten localization and abelianization for qde solutions
Abstract
We prove a quantum version of the localization formula of Witten that relates invariants of a git quotient with the equivariant invariants of the action. Using the formula we prove a quantum version of an abelianization formula of S. Martin relating invariants of geometric invariant theory quotients by a group and its maximal torus, conjectured by Bertram, Ciocan-Fontanine, and Kim. By similar techniques we prove a quantum Lefschetz principle for holomorphic symplectic reductions. As an application, we give a formula for the fundamental solution to the quantum differential equation (qde) for the moduli space of points on the projective line and for the smoothed moduli space of framed sheaves on the projective plane (a Nakajima quiver variety).
Cite
@article{arxiv.0811.3358,
title = {Quantum Witten localization and abelianization for qde solutions},
author = {Eduardo Gonzalez and Chris Woodward},
journal= {arXiv preprint arXiv:0811.3358},
year = {2016}
}
Comments
41 pages. A previous version was called "Area-dependence in gauged Gromov-Witten theory". Some of that material was moved into "Wall-crossing for Gromov-Witten invariants under variation of git quotient", while some new material was added