Spherical membranes in Matrix theory

Kabat, Daniel; Taylor, Washington

Spherical membranes in Matrix theory

Authors

Description

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.
21 pages LaTeX. V2: references added; V3: reference added, minor corrections