Study the Role of R2 Term in Cosmological AdS-like Space by AdS/CFT Correspondence.

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]