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For pure single-trace diagrams the values of F (G) have been computed in Table 1 in [24], so we can utilize their results. 4. Let us illustrate by showing the computations for (a). There is a total of four index loops and hence h = 4 for this diagram. Moreover, since it is composed of the pasting of two primitive diagrams each of which has h = 2; thus, we have C(G) = 2 × 2 = 4. Finally, F = g2 because there is only one contraction possible, viz, Tr(ΦΦ)Tr(ΦΦ). 4: All two-loop primitive and pasting diagrams.

In Poincare coordinate the boundary is at z = 0. 7) We can then vary the generating function with respect to the source φ0 (x) to computed correlation functions of corresponding operators. 7), the cor55 relation function can also be computed from the string theory side by varying the supergravity action with respect to boundary fields. The AdS/CFT correspondence is a strong-weak duality. In the regime that classical supergravity is valid, the gauge theory is strongly coupled and the corresponding physical quantities can not be computed by gauge pertuabation theory.

Furthermore, on this sub-manifold of the Coulomb branch, the tree-level superpotential has to be minimized to find the N = 1 vacua. By varying the parameters of the superpotential, these N = 1 vacua can be moved around on the Coulomb branch of N = 2 moduli space. In particular, special corners in the parameter space will place these vacua in regions where the 44 U(N) gauge symmetry breaking scale is much greater than Λ, the N = 2 dynamical scale. Thus the gauge group is higgsed. These regions can then be analyzed by weak coupling analysis.

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