  The gauge/gravity duality conjecture claims the equivalence between gauge
theory and superstring/M-theory. In particular, the one-dimensional gauge
theory of D0-branes and type IIA string theory should agree on properties of
hot black holes. Type IIA superstring theory predicts the leading $N^2$
behavior of the black hole internal energy to be $E/N^2=a_0T^{14/5}+
a_1T^{23/5}+a_2T^{29/5}+\cdots$ with the supergravity prediction $a_0=7.41$ and
unknown coefficients $a_1$, $a_2$, $\ldots$ associated with stringy
corrections. In order to test this duality we perform a lattice study of the
gauge theory and extract a continuum, large-$N$ value of $a_0=7.4\pm 0.5$---the
first direct confirmation of the supergravity prediction at finite
temperature---and constrain the stringy corrections ($a_1=-9.7\pm2.2$ and
$a_2=5.6\pm1.8$). We also study the sub-leading $1/N^2$ corrections to the
internal energy.
