67 Chapter 2: Motivation temperature. The first comes from the usual counting of states with 6 N 2 massless scalars and 4 N 2 massless Weyl fermions. Taking the spatial volume of the 3-brane to be V$_{3}$ we have The Bekenstein-Hawking relation, S$_{BH}$ = A/ 4 G$_{N}$ , gives the entropy of the black p brane in the supergravity picture. The 8-dimensional area of the horizon may be read off of Eq. (2.63) as S = 2 π 3 3 N $^{2}$V$_{3}$ T $^{3}$. (2.65) A = ( r$_{0}$ R$^{)}$$^{3}$ V$_{3}$R $^{5}$Ω$_{5}$ = π $^{6}$V$_{3}$ R $^{8}$T $^{3}$, (2.66) S$_{BH}$ = A 4 G$_{N}$ = π 2 2 N $^{2}$V$_{3}$ T $^{3}$. (2.67) where the second equality comes from Eq. (2.64). By Eq. (2.46) G (10) N = 8 π $^{6}$g2 $_{s}$l 8 s = π $^{4}$R$^{8}$/ (2 N $^{2}$), so The factor of 4 / 3 difference between the weakly-coupled and black hole entropy limits is a prediction for the change in the number of degrees of freedom from weakly-coupled SU ( N ) to strongly-coupled SU ( N ). This provides a natural explanation for the discrepancy of about 20% between lattice results at a few times T$_{c}$ , still at strong coupling, and the expected weak-coupling Stefan- Boltzmann limit as seen in Fig. 1.6 (b). One may next find the strong coupling limit for the entropy to viscosity