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.

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!

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Cited by in corpus (11)

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• Reformulating Supersymmetry with a Generalized Dolbeault Operator
• T-duality, Gerbes and Loop Spaces
• Courant-like brackets and loop spaces
• The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction
• Gauging the Poisson sigma model
• p-Brane Actions and Higher Roytenberg Brackets
• Supersymmetry of the chiral de Rham complex II: Commuting Sectors
• Generalized Almost Product Structures and Generalized CRF-structures
• An Alternative Topological Field Theory of Generalized Complex Geometry
• Polynomial Structures in Generalized Geometry