Spherical membranes in Matrix theory

Abstract

We consider membranes of spherical topology in uncompactified Matrix theory. In general for large membranes Matrix theory reproduces the classical membrane dynamics up to 1/N corrections; for certain simple membrane configurations, the equations of motion agree exactly at finite N. We derive a general formula for the one-loop Matrix potential between two finite-sized objects at large separations. Applied to a graviton interacting with a round spherical membrane, we show that the Matrix potential agrees with the naive supergravity potential for large N, but differs at subleading orders in N. The result is quite general: we prove a pair of theorems showing that for large N, after removing the effects of gravitational radiation, the one-loop potential between classical Matrix configurations agrees with the long-distance potential expected from supergravity. As a spherical membrane shrinks, it eventually becomes a black hole. This provides a natural framework to study Schwarzschild black holes in Matrix theory.