Brackets, Sigma Models and Integrability of Generalized Complex Structures
Abstract
It is shown how derived brackets naturally arise in sigma-models via Poisson- or antibracket, generalizing a recent observation by Alekseev and Strobl. On the way to a precise formulation of this relation, an explicit coordinate expression for the derived bracket is obtained. The generalized Nijenhuis tensor of generalized complex geometry is shown to coincide up to a de-Rham closed term with the derived bracket of the structure with itself, and a new coordinate expression for this tensor is presented. The insight is applied to two known two-dimensional sigma models in a background with generalized complex structure. Introductions to geometric brackets on the one hand and to generalized complex geometry on the other hand are given in the appendix.
Cite
@article{arxiv.hep-th/0609015,
title = {Brackets, Sigma Models and Integrability of Generalized Complex Structures},
author = {Sebastian Guttenberg},
journal= {arXiv preprint arXiv:hep-th/0609015},
year = {2010}
}
Comments
48 pages (27 without appendix), created with LyX, based on LaTeX, including hyperrefs. Typos in (2.162)-(2.167) and in (3.15) fixed. Content agrees with JHEP-Version. Page numbers and equation numbers agree with old version but not with JHEP version!