In the context of guage/gravity duality, we investigate the central charges of a number of 2-dimensional conformal field theories (CFTs) that might live on the boundary of some 3-dimensional (3D) toy models of gravity, from the thermodynamics aspect of the black holes. For many black hole solutions, the entropy product of the inner Cauchy and outer event horizons is universal (mass independent). It is proposed that for these solutions, the central charges of the left- and right-moving sectors of the dual CFTs should be the same and one may read the central charges from the universal entropy product. This provides strong motivations for investigating this prescription for BTZ and Warped \(\hbox {AdS}_{{3}}\) black holes in a number of 3D gravity theories and we will show that the proposal works truly. One striking result of our analysis is that if the entropy product is not universal in any theory of 3D gravity, then the left and right central charges are not equal.

中文翻译：

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3D重力作用下热力学方法产生的中心电荷

在量规/重力对偶的背景下，我们从热力学方面研究了可能存在于某些3D（3D）重力玩具模型边界上的2D保形场理论（CFT）的中心电荷黑洞。对于许多黑洞解，内部柯西层和外部事件层的熵乘积是通用的（与质量无关）。建议对于这些解决方案，双重CFT的左，右移动扇区的中心电荷应相同，并且可以从通用熵乘积中读取中心电荷。这为调查BTZ和扭曲的\（\ hbox {AdS} _ {{3}} \）的处方提供了强大的动力。许多3D重力理论中都存在黑洞，我们将证明该建议确实有效。我们的分析的一个惊人结果是，如果熵乘积在任何3D重力理论中都不是通用的，则左右中心电荷不相等。