Normal Coordinates in Kahler Manifolds and the Background Field Method
High Energy Physics - Theory
2009-11-07 v3 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
Riemann normal coordinates (RNC) are unsuitable for \kahler manifolds since they are not holomorphic. Instead, \kahler normal coordinates (KNC) can be defined as holomorphic coordinates. We prove that KNC transform as a holomorphic tangent vector under holomorphic coordinate transformations, and therefore that they are natural extensions of RNC to the case of \kahler manifolds. The KNC expansion provides a manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models.
Cite
@article{arxiv.hep-th/0203081,
title = {Normal Coordinates in Kahler Manifolds and the Background Field Method},
author = {Kiyoshi Higashijima and Etsuko Itou and Muneto Nitta},
journal= {arXiv preprint arXiv:hep-th/0203081},
year = {2009}
}
Comments
LaTeX2e, 24 pages, no figures, the version to appear in Prog. Theor. Phys. 108