content_image/297795.jpg content_image/297794.jpg content_image/297793.jpg content_image/297792.jpg
Then we need to consider 

<img src='content_image/297795.jpg'>

We have been able to pick out the smallest energy eigenvalue E$_{0}$ in (4.9) because in the T → ∞ limit, it will dominate all the other terms. 

All we have left to do to demonstrate (4.7) is to show that lim T →∞ Ω( T, R ) ∼ lim T →∞ W ( C ). However, the Wilson loop corresponds to an extended ‘source’ in the fundamental representation (ie. quarks), separated by a distance R , being created at T = 0 and annihilated at some general T , so we are done. 

Let us apply equation (4.6) to the Constable-Myers geometry considered in this chapter. The Nambu-Goto action of the fundamental string is [109]: 

<img src='content_image/297794.jpg'>

with G$_{MN}$ denoting the string frame metric, which is related to the Einstein metric by a scaling factor: 

<img src='content_image/297793.jpg'>

It will be useful to recast (4.11) with an explicit 5-sphere symmetry: 

<img src='content_image/297792.jpg'>

