Born-Infeld Actions from Matrix Theory

We propose a formula for the effective action of Matrix Theory which succesfully reproduces a large class of Born-Infeld type D-brane probe actions. The formula is motivated by demanding consistency with known results, and is tested by comparing with a wide range of source-probe calculations in supergravity. In the case of D0-brane sources and Dp-brane probes, we study the effect of boosts, rotations, and worldvolume electric fields on the probe, and find agreement with supergravity to all orders in the gravitational coupling. We also consider D4-brane sources at the one loop level and recover the correct probe actions for a D0-brane, and for a D4-brane rotated at an angle with respect to the source