$L^p$-Analysis of the Hodge--Dirac operator associated with Witten Laplacians on complete Riemannian manifolds

We prove $R$-bisectoriality and boundedness of the $H^{\mathrm{\infty }}$-functional calculus in $L^p$ for all $1<p<\mathrm{\infty }$ for the Hodge-Dirac operator associated with Witten Laplacians on complete Riemannian manifolds with non-negative Bakry-Emery Ricci curvature on $k$-forms.