Conjecture on the Costello–Li twist and the Courant contact model

Let $\mathcal E_{\mathrm{twist}}$ be the Courant algebroid over the Dolbeault complex associated to a twist datum. The Costello–Li twist of type I supergravity is the perturbative Batalin–Vilkovisky theory obtained by expanding the supergravity BV action around the corresponding critical point. Conjecture. The Costello–Li twist of type I supergravity should be equivalent as a perturbative BV theory to the Courant contact model for $\mathcal E_{\mathrm{twist}}$. This is a precise formulation of the proposed comparison between the twisted supergravity theory and the Courant-algebroid model; it is not proved in the paper.