Matrix Theory Star Products from the Born–infeld Action

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 α′, 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 α′, 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. E-mail: [email protected] – After Oct. 1st: I.H.E.S., Le Bois-Marie, Bures-Sur-Yvette, 91440 France E-mail: [email protected] – After Sep. 1st: Dept. Physics, Harvard University, Cambridge, MA 02138