  In this note, we obtain new obstructions to symplectic embeddings of a
product of disks (a polydisk) into a 4-dimensional ball. The polydisk P(r,s) is
the product of the disk of area r with the disk of area s. The ball of capacity
a, denoted B(a), is the ball with \pi r^2 \le a.
  We show P(1,2) embeds in B^4(a) if and only if a is at least 3. This shows
the inclusion of P(1,2) in B^4(3) is optimal. The necessity of a \ge 3 implies
that for this particular embedding problem neither the Ekeland-Hofer nor ECH
capacities give a sharp obstruction. We contrast this with the case of
ellipsoid embeddings into a ball when the ECH capacities give a complete list
of obstructions [McDuff 2011]. Our obstruction does not come from a symplectic
capacity, but instead from pseudoholomorphic foliations, thus the techniques
seem to be special to dimension 4.
