2d gauge theories and generalized geometry

We show that in the context of two-dimensional sigma models minimal coupling
of an ordinary rigid symmetry Lie algebra g leads naturally to the appearance of the
“generalized tangent bundle” TM ≡ T M ⊕ T ∗ M by means of composite fields. Gauge
transformations of the composite fields follow the Courant bracket, closing upon the choice
of a Dirac structure D ⊂ TM (or, more generally, the choide of a “small Dirac-Rinehart
sheaf” D), in which the fields as well as the symmetry parameters are to take values. In
these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma
model, which is applicable in a more general context and proves to be universal in two
space-time dimensions: a gauging of g of a standard sigma model with Wess-Zumino term
exists, iff there is a prolongation of the rigid symmetry to a Lie algebroid morphism from
the action Lie algebroid M × g → M into D → M (or the algebraic analogue of the
morphism in the case of D). The gauged sigma model results from a pullback by this
morphism from the Dirac sigma model, which proves to be universal in two-spacetime
dimensions in this sense.