Spectrum of LargeNGauge Theory from Supergravity

Recently, Maldacena proposed that the large $N$ limit of the $N=4\mathrm{}$ supersymmetric gauge theory in four dimensions with $\mathrm{U}\left(N\right)$ gauge group is dual to the type IIB superstring theory on ${\mathrm{AdS}}_5\times S^5$. We use this proposal to study the spectrum of the large $N$ gauge theory on $ℝ\times S^3$ in a low energy regime. We find that the spectrum is discrete and evenly spaced, and the number of states at each energy level is smaller than the one predicted by the naive extrapolation of the Bekenstein-Hawking formula to the low energy regime. We also show that the gauge theory describes a region of spacetime behind the horizon as well as the region in front.