instead of just considering the duality as being constructed on the boundary of the AdS$_{5}$ × S 5 space, we are free to look at the duality at any value of r : each different choice of r simply represents the same field theory at a different energy scale. From here onwards, the r coordinate is referred to as the energy scale. The small r limit is called the infrared (IR), and the high r limit is called the UV (ultraviolet). The correspondence will only be useful if there is a prescribed way of cal- culating physical quantities on each side. The way to do this was first suggested in [55], and the postulate is that the generating functional for correlation functions with some source φ$_{0}$ ( x ) is equal to the supergravity partition function whose fields φ ( x ) tend to φ$_{0}$ ( x ) at the boundary of the AdS$_{5}$ × S 5 space: So, in simple terms, the boundary values for supergravity fields correspond to sources for the field theory operators. The LHS side of (2.9) is independent of the global symmetries of the conformal field theory. So, the entity ∫ d $^{4}$x φ$_{0}$ ( x ) O ( x ) must be a singlet under all the symmetries of the dual field theory. This is how we go about identifying which fields in the supergravity match with which operators in the CFT, which we address next. 41 2.6 Explicit Correspondence 〈 Exp (∫ d $^{4}$xφ$_{0}$ ( x ) O ( x ) ) 〉 AdS 5 × S 5 ∣ φ ( x, ∞ )= φ 0 ( x ) = Z $_{string}$[ φ$_{0}$ ( x )] (2.9)