Reidemeister torsion for flat superconnections

We use higher parallel transport-more precisely, the integration -functor constructed in Arias Abad and Schatz (The 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-Muller theorem, namely that the combinatorial Reidemeister torsion coincides with the analytic torsion defined by Mathai and Wu (Contemp Math 546, 199-212, 2011).