Infinitesimal symmetries of bundle gerbes and Courant algebroids

Let M be a smooth manifold and let \(\chi \in \Omega ^3(M)\) $\chi \in {\mathrm{\Omega }}^3(M)$ be closed differential form with integral periods. We show the Lie 2-algebra \(\mathbb {L}(C_\chi )\) $\mathbb{L}(C_{\chi })$ of sections of the \(\chi \) $\chi$ -twisted Courant algebroid \(C_\chi \) $C_{\chi }$ on M is quasi-isomorphic to the Lie 2-algebra of connection-preserving multiplicative vector fields on an \(S^1\) $S^1$ -bundle gerbe with connection (over M) whose 3-curvature is \(\chi \) $\chi$ .