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It has been shown that AdS/CFT correspondence may be realized between some AdS-like cosmological space and CFT living on the boundary. By extending such works we studied the role of R2 term in the corrected action to the thermodynamic quantities, particularly by adding a boundary counterterms to the gravitational action and considering an AdS-like cosmological space. With such HD (higher derivative) terms and metric we calculated the free energy, as a function of N2T4 times 3/2(1 − 1/N2), that is comparable with perturbative result followed from boundary QFT. In fact the difference between the results obtained from AdS-like cosmological space and the results obtained from strong coupling limit of ℵ = 4 SCFT, by taking into account next to leading term in large N expansion, is just a 3/2 factor. Higher derivative term contributions also appear in entropy and energy via the redefinition of gravitation constant. We explicitly identify higher order counterterms effect in energy as a constant term namely E0. This value can be interpreted as the Casimir energy, so that, there is a full and perfect match between QFT and gravitational action when both R2 term and boundary counterterms are considered. So we can claim that our results have assured us that there is a good fit between AdS-like cosmological space and ℵ = 4 SU(N) super Yang-Mills quantum theory. [ABSTRACT FROM AUTHOR]

Gravitational perturbation in AdS4, decomposed into axial and polar perturbations that have different parities. After imposing geometric perturbation in to the spherical, symmetric and static metric of AdS4, we can calculate the possible spectrum of frequencies around the static configuration. This spectrum relates to the boundary conditions imposed at spatial infinity ( r=∞) and will be implied by the wave function’s behavior at $x=\frac{\pi}{2}$ or y=1. At the end we write down the first order raising and lowering operators from the second order Schrödinger equation to study the supersymmetry model and check whether we have supersymmetric partners or no. After finding the H1 and the partner H2, we check the supersymmetry. At the end, we find the potentials to confirm the shape invariance condition and also the supercharges and their commutative relations are studied. [ABSTRACT FROM AUTHOR]