Hamiltonian perspective on generalized complex structure

TL;DR

This paper explores the connection between extended world-sheet supersymmetry in sigma models and generalized complex structures, using phase space analysis and automorphism groups to clarify their geometric relationship.

Contribution

It provides a new perspective on the relation between supersymmetry and generalized complex geometry through the phase space approach and automorphism group analysis.

Findings

Identifies the isomorphism between automorphisms of the Courant bracket and local canonical transformations.

Explains the relation between world-sheet supersymmetry and generalized complex structures.

Discusses implications for D-branes within this geometric framework.

Abstract

In this note we clarify the relation between extended world-sheet supersymmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism between the group of orthogonal automorphisms of the Courant bracket and the group of local canonical transformations of the cotangent bundle of the loop space. Indeed this fact explains the natural relation between the world-sheet and the geometry of T+T^*. We discuss D-branes in this perspective.