Mathematics

A sigma model is a theory of maps between manifolds. The model has supersymmetry if the target manifold carries certain geometrical structures. Focusing on the particular case of (2,2) supersymmetry, the target manifold has a generalized Kaehler structure. In this talk, I will introduce and define each of the terms above. Generalized geometry is a reformulation of differential geometry taking place on the direct sum of the tangent and cotangent bundles rather than just the tangent bundle. Complex structures in generalized geometry generalize both complex and symplectic geometry. The analog of the Kaehler condition is having two commuting generalized complex structures. I will show how the sigma model formulation predicts the existence of a single local function describing the entire generalized Kaehler structure, as in the usual Kaehler case.