  In this paper we study the general conditions that have to be met for a
gauged extension of a two-dimensional bosonic sigma-model to exist. In an
inversion of the usual approach of identifying a global symmetry and then
promoting it to a local one, we focus directly on the gauge symmetries of the
theory. This allows for action functionals which are gauge invariant for rather
general background fields in the sense that their invariance conditions are
milder than the usual case. In particular, the vector fields that control the
gauging need not be Killing. The relaxation of isometry for the background
fields is controlled by two connections on a Lie algebroid L in which the gauge
fields take values, in a generalization of the common Lie-algebraic picture.
Here we show that these connections can always be determined when L is a Dirac
structure in the H-twisted Courant algebroid. This also leads us to a
derivation of the general form for the gauge symmetries of a wide class of
two-dimensional topological field theories called Dirac sigma-models, which
interpolate between the G/G Wess-Zumino-Witten model and the (Wess-Zumino-term
twisted) Poisson sigma model.
