Schwarzschild Black Holes from Matrix Theory

We consider matrix theory compactified on T³ and show that it correctly describes the properties of Schwarzschild black holes in $7+1$ dimensions, including the mass-entropy relation, the Hawking temperature, and the physical size, up to numerical factors of order unity. The most economical description involves setting the cutoff N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for $3+1$ dimensional supersymmetric Yang-Mills theory with 16 supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski.