Lectures on Generalized Complex Geometry and Supersymmetry

Abstract

These are the lecture notes from the 26th Winter School "Geometry and Physics", Czech Republic, Srni, January 14 - 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely to two-dimensional field theories. We explain in detail the relation between generalized complex geometry and supersymmetry. We briefly review the generalized Kahler and generalized Calabi-Yau manifolds and explain their appearance in physics.

34 pages, the lecture notes from the Winter School "Geometry and Physics", January 14-21, 2006, Srni, Czech Republic

References in corpus (3)

• Topological sigma-models with H-flux and twisted generalized complex manifolds
• On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case
• A brief review of supersymmetric non-linear sigma models and generalized complex geometry

Cited by in corpus (33)

• Lectures on Generalized Complex Geometry for Physicists
• Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
• T-duality and Generalized Kahler Geometry
• Poisson sigma model on the sphere
• The biHermitian topological sigma model
• Generalizing Geometry - Algebroids and Sigma Models
• Generalized Hyperkaehler Geometry and Supersymmetry
• Courant-like brackets and loop spaces
• A potential for Generalized Kahler Geometry
• The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction
• Brackets, Sigma Models and Integrability of Generalized Complex Structures
• Generalized Calabi-Yau manifolds and the chiral de Rham complex
• 2d Gauge Theories and Generalized Geometry
• Chiral de Rham complex on Riemannian manifolds and special holonomy
• p-Brane Actions and Higher Roytenberg Brackets
• Semichiral Fields on S^2 and Generalized Kähler Geometry
• Generalised HyperKaehler Manifolds in String Theory
• Stochastic deformation of a thermodynamic symplectic structure
• T-duality and Generalized Complex Geometry
• Dirac structures on generalized Riemannian manifolds
• Fluctuations as stochastic deformation
• Integrable Hopf twists, marginal deformations and generalised geometry
• Generalized Cohomologies and Supersymmetry
• On flux vacua, SU(n)-structures and generalised complex geometry
• Gauged Supergravities and the Physics of Extra Dimensions
• Generalized geometry lectures on type II backgrounds
• Exotic Courant algebroids and T-duality
• Commuting Pairs, Generalized para-Kähler Geometry and Born Geometry
• Geometry on Big-Tangent Manifolds
• Flux Backgrounds and Exceptional Generalised Geometry
• Tensionless Strings and Supersymmetric Sigma Models: Aspects of the Target Space Geometry
• Strings as sigma models and in the tensionless limit
• Generalized K$\ddot{a}$hler Geometry in Kazama-Suzuki coset models