Spherical membranes in m(atrix) theory

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 iV, but differs at subleading orders in N. The result is quite general: we prove a pair of theorems showing that for large TV, 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. 1 kabat@ias.edu 2 wati@princeton.edu 182 SPHERICAL MEMBRANES IN M(ATRIX) THEORY

[1]  S. D. Alwis.  A note on brane tension and M-theory , 1996, hep-th/9607011.

[2]  Matrix black holes , 1997, hep-th/9703211.

[3]  E. Keski-Vakkuri,et al.  Born-Infeld actions from Matrix theory , 1997, hep-th/9709122.

[4]  Schwarzschild black holes in various dimensions from matrix theory , 1997, hep-th/9709108.

[5]  Five-branes in M(atrix) Theory , 1996, hep-th/9610236.

[6]  J. Polchinski,et al.  Higher order graviton scattering in M(atrix) theory , 1997, hep-th/9706072.

[7]  Why Is the Matrix Model Correct , 1997, hep-th/9710009.

[8]  S. Shenker,et al.  Branes from matrices , 1996, hep-th/9612157.

[9]  M theory as a matrix model: A Conjecture , 1996, hep-th/9610043.

[10]  L. Susskind,et al.  Schwarzschild black holes in matrix theory II , 1998 .

[11]  Another Conjecture about M(atrix) Theory , 1997, hep-th/9704080.

[12]  W. Taylor,et al.  Linearized supergravity from Matrix theory , 1997, hep-th/9712185.

[13]  I. Chepelev,et al.  Long-distance interactions of branes: Correspondence between supergravity and super Yang-Mills descriptions , 1997, hep-th/9709087.

[14]  S. Ramgoolam,et al.  Branes, fluxes and duality in M(atrix)-theory , 1996, hep-th/9611202.

[15]  J. Maldacena.  Branes probing black holes , 1997, hep-th/9709099.

[16]  D0-branes on $T^n$ and matrix theory , 1997, hep-th/9709220.

[17]  J. Polchinski,et al.  Compactification in the lightlike limit , 1997, hep-th/9711037.

[18]  Probing near extremal black holes with D -branes , 1997, hep-th/9705053.

[19]  L. Susskind,et al.  Schwarzschild Black Holes from Matrix Theory , 1998 .

[20]  Chaos in M(atrix) theory , 1997, hep-th/9710032.

[21]  H. Ooguri,et al.  Why Matrix Theory is Hard , 1997, hep-th/9710178.

[22]  D-branes and short distances in string theory , 1996, hep-th/9608024.

[23]  M. Dine,et al.  Multigraviton scattering in the matrix model , 1997, hep-th/9710174.

[24]  A two-loop test of M(atrix) theory , 1997, hep-th/9705091.