Figure 2.14: (a) Heavy q ¯ q potential for N$_{c}$ = 3 and λ = 10 (blue, dotted), 10 2 (green, short dash), 10 3 (red, long dash), and 10 4 (black, solid). As λ → ∞ the potential develops a kink at | x | = . 24 /T ; for larger distances the potential continues to rise, but very slowly. Figure adapted from [337]. (b) The AdS/CFT scaled energy density of the SYM plasma with Mach cone for a heavy quark with v = 3 / 4 . Figure adapted from [341]. 2.3.5 Testing the Conjecture The most well known result of using this complicated machinery is the famous viscosity to entropy bound [332, 335] As noted earlier, qualitative estimates of the viscosity at$_{Rhic}$ [121] appear to require such small values of η/s . This encourages continued investigation of applications of the AdS/CFT conjecture, but the big question is: how much can we trust the AdS/CFT results? The duality of N = 4 SYM and Type IIB string theory on a pure AdS$_{5}$ × S 5 background has strong motivation and passed η s = 1 4 π$^{(}$ 1 + O ( 1 √ λ )$^{)}$ . (2.70) 70 Chapter 2: Motivation (a) (b)