Abstract
We discuss a natural extension of the AKSZ construction to the case where the source is given by a supermanifold with a chosen integral form. We then focus on the special case with the target given by a Courant algebroid. In the simplest case this leads to the BV version of the super Chern-Simons theory, as developed by Grassi-Maccaferri and Cremonini-Grassi. In the case of exact Courant algebroids we derive the 2-dimensional mathcal{N} = (1, 1) sigma model on the boundary, together with the Wess-Zumino term, paralleling the approach of Ševera in the bosonic case.
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