  The superfluid-insulator transition of bosons is strongly modified by the
presence of Fermions. Through an imaginary-time path integral approach, we
derive the self-consistent mean-field transition line, and account for both the
static and the dynamic screening effects of the fermions. We find that an
effect akin to the fermionic orthogonality catastrophe, arising from the
fermionic screening fluctuations, suppresses superfluidity. We analyze this
effect for various mixture parameters and temperatures, and consider possible
signatures of the orthogonality catastrophe effect in other measurables of the
mixture.
