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.

已经表明，在一些类似 AdS 的宇宙空间和生活在边界上的 CFT 之间可以实现 AdS/CFT 对应。通过扩展这些工作，我们研究了R ²项在热力学量的校正作用中的作用，特别是通过向引力作用添加边界反项并考虑类似 AdS 的宇宙学空间。使用这样的 HD（高导数）项和度量，我们计算了自由能，作为N ² T ⁴乘以 3/2(1 − 1/ N ²)，这与从边界 QFT 得到的微扰结果相当。事实上，从类似 AdS 的宇宙学空间获得的结果与从ℵ = 4 SCFT 的强耦合极限获得的结果之间的差异，通过考虑大 N 扩展中的次要项，只是一个 3/2 的因素。通过重新定义引力常数，更高的微分项贡献也出现在熵和能量中。我们明确地将能量中的高阶反项效应确定为常数项，即E ₀。这个值可以解释为 Casimir 能量，因此，当R ²考虑术语和边界反术语。所以我们可以声称我们的结果已经向我们保证了类似 AdS 的宇宙学空间和ℵ = 4 SU(N) 超级杨米尔斯量子理论之间有很好的拟合。