content_image/357389.jpg
<img src='content_image/357389.jpg'>

For attractive bosons it drops below it by a factor of 0 . 4, however this could be an artifact of our approximation. For attractive fermions, the conjectured lower bound is reached at very large µ/T ≈ 10 $^{7}$, however this was argued to occur in an unphysical or metastable region; in the physical regions, η/s ≥ 6 . 07 ℏ / 4 πk$_{B}$ . 

## XI. ACKNOWLEDGMENTS 

We thank Erich Mueller for helpful discussions. This work is supported by the National Science Foundation under grant number NSF-PHY-0757868. 

