  We show that in the context of two-dimensional sigma models minimal coupling
of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the
appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus
T^*M$ by means of composite fields. Gauge transformations of the composite
fields follow the Courant bracket, closing upon the choice of a Dirac structure
$D \subset \mathbb{T}M$ (or, more generally, the choide of a "small
Dirac-Rinehart sheaf" $\cal{D}$), 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 $\mathfrak{g}$ of a standard sigma model with Wess-Zumino term
exists, \emph{iff} there is a prolongation of the rigid symmetry to a Lie
algebroid morphism from the action Lie algebroid $M \times \mathfrak{g}\to M$
into $D\to M$ (or the algebraic analogue of the morphism in the case of
$\cal{D}$). 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.
