Hamiltonian perspective on generalized complex structure

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.

14 pages, the version to appear in CMP

References in corpus (13)

• A path integral approach to the Kontsevich quantization formula
• Topological strings on noncommutative manifolds
• Current Algebras and Differential Geometry
• Generalized complex manifolds and supersymmetry
• Topological sigma-models with H-flux and twisted generalized complex manifolds
• Vertex Algebras, Mirror Symmetry, And D-Branes: The Case Of Complex Tori
• Generalized N=(2,2) Supersymmetric Non-Linear Sigma Models
• Generalized complex geometry, generalized branes and the Hitchin sigma model
• Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
• A sigma model field theoretic realization of Hitchin's generalized complex geometry
• N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models
• Actions For (2,1) Sigma-Models and Strings
• Geometry of D-branes for general N=(2,2) sigma models

Cited by in corpus (39)

• Generalized structures of N=1 vacua
• The Hitchin functionals and the topological B-model at one loop
• Lectures on Generalized Complex Geometry and Supersymmetry
• Generalized Kahler Geometry from supersymmetric sigma models
• T-duality and Generalized Kahler Geometry
• The biHermitian topological sigma model
• A topological sigma model of biKaehler geometry
• Generalized Hyperkaehler Geometry and Supersymmetry
• First-order supersymmetric sigma models and target space geometry
• New N = (2, 2) vector multiplets
• Brackets, Sigma Models and Integrability of Generalized Complex Structures
• Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry
• Chiral de Rham complex on Riemannian manifolds and special holonomy
• Flux Vacua and Supermanifolds
• D-brane on Poisson manifold and Generalized Geometry
• Twistor spaces of generalized complex structures
• Black hole entropy and topological strings on generalized CY manifolds
• Generalised HyperKaehler Manifolds in String Theory
• BiHermitian Supersymmetric Quantum Mechanics
• A brief review of supersymmetric non-linear sigma models and generalized complex geometry
• The Large Vector Multiplet Action
• Hyperkähler, Bi-hypercomplex, Generalized Hyperkähler Structures and T-duality
• T-duality and Generalized Complex Geometry
• Complex Structures, T-duality and Worldsheet Instantons in Born Sigma Models
• Topological twisted sigma model with H-flux revisited
• An Alternative Topological Field Theory of Generalized Complex Geometry
• Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds
• Brane current algebras and generalised geometry from QP manifolds
• Tensionless Strings and Supersymmetric Sigma Models: Aspects of the Target Space Geometry
• Generalized K$\ddot{a}$hler Geometry and current algebras in classical N=2 superconformal WZW model
• Generalized Kähler Geometry and current algebras in $SU(2)\times U(1)$ N=2 superconformal WZW model
• Poisson sigma models on surfaces with boundary: classical and quantum aspects
• Strings as sigma models and in the tensionless limit
• Derived Brackets from Super-Poisson Brackets
• Generalized K$\ddot{a}$hler Geometry in Kazama-Suzuki coset models
• Non-linear sigma models via the chiral de Rham complex
• Doubled space and extended supersymmetry
• Conformal Euler-Lagrangian Equations on Para-Quaternionic Kahler Manifolds
• Lagrangian and Hamiltonian Mechanical Systems on Para-Quaternionic Kaehler Manifolds