  We conjecture that the Sen-Seiberg limit of the Type IIA D2-brane action in a
flat spacetime background can be resummed, at all orders in \alpha', to define
an associative star product on the membrane. This star product can be
independently constrained from the equivalent Matrix theory description of the
corresponding M2-brane, by carefully analyzing the known BPS conditions. Higher
derivative corrections to the Born-Infeld action on the IIA side are
reinterpreted, after the Sen-Seiberg limit, as higher derivative corrections to
a field theory on the membrane, which itself can be resummed to yield the known
Matrix theory quantum mechanics action. Conversely, given the star product on
the membrane as a formal power series in \alpha', one can constrain the higher
derivative corrections to the Born-Infeld action, in the Sen-Seiberg limit.
This claim is explicitly verified to first order. Finally, we also comment on
the possible application of this method to the derivation of the Matrix theory
action for membranes in a curved background.
