Topological quantum field theory and hyperk\"ahler geometry
Quantum Algebra
2009-04-03 v1 Differential Geometry
Abstract
Rozansky and Witten proposed a 3-dimensional sigma-model whose target space is a hyperk\"ahler manifold. They conjectured that this theory has an associated TQFT, with Hilbert spaces given by certain cohomology groups of the hyperk\"ahler manifold. On the other hand, there is a certain modified TQFT constructed by Murakami and Ohtsuki using the universal quantum invariant. We explain how the Rozansky-Witten TQFT can be obtained from the latter by applying a `hyperk\"ahler weight system'.
Keywords
Cite
@article{arxiv.math/0009222,
title = {Topological quantum field theory and hyperk\"ahler geometry},
author = {Justin Sawon},
journal= {arXiv preprint arXiv:math/0009222},
year = {2009}
}
Comments
LaTeX, 26 pages, 13 figures; submitted to Proceedings of 7th Gokova Geometry-Topology Conference (2000), uses gokova.cls and goksty.tex