Comment on "Exact bosonization for an interacting fermi gas in arbitrary dimensions".

In a recent Letter [1], Efetov et al. propose an exact mapping of an interacting fermion system onto a new model that is supposed to allow sign-problem-free Monte Carlo simulations. In this Comment, we show that their formalism is equivalent to the standard approach of Blackenbecker, Scalapino, and Sugar (BSS) [2] for fermi-onic systems and has the same sign statistics and minus sign problem. Our first observation is that the partition function for a given configuration of the auxiliary fields is the same in the standard formulation Z f [Eq. (8) in Ref. [1]] and in their new bosonized scheme Z b [Eq. (9)]: Z f ½Š ¼ Z b ½Š: (1) This observation is trivial in the limit of the time step Á ! 0, where both schemes reproduce the same partition function. Since Z f can be negative also in this limit [2], Z b is also not sign positive. Both Z f and Z b are positive if is a smooth path [2], but restricting the configuration space to smooth paths amounts to a semiclassical approximation. We next show that Z f ½Š ¼ Z b ½Š also holds for finite Á and piecewise constant paths where the field r ðÞ is constant on the interval ½ðl þ 1ÞÁ; lÁŠ. Efetov et al.'s Eq.