Reidemeister torsion for flat superconnections

We use higher parallel transport—more precisely, the integration A∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf{A }_\infty $$\end{document}-functor constructed in Arias Abad and Schätz (The A∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf{A}_\infty $$\end{document} de Rham theorem and the integration of representations up to homotopy. Int Math Res Not, 2013) and Block and Smith (A Riemann–Hilbert correspondence for infinity local systems. arXiv:0908.2843, 2012)—to define Reidemeister torsion for flat superconnections. We conjecture a version of the Cheeger–Müller theorem, namely that the combinatorial Reidemeister torsion coincides with the analytic torsion defined by Mathai and Wu (Contemp Math 546, 199–212, 2011).