双荷伸缩子AdS黑洞的全息热力学
Holographic Thermodynamics of Dyonic Dilaton AdS Black Holes
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中文总结 AI 辅助
研究双荷伸缩子AdS黑洞的扩展体热力学全息对偶，通过变动宇宙学常数与牛顿引力常数，分析多类系综的相变特征，揭示引力参数变化对应CFT的临界现象与丰富相结构。
中文摘要 AI 辅助
我们通过允许宇宙学常数与牛顿引力常数同时变动，研究双荷伸缩子AdS黑洞扩展体热力学的全息对偶。在对偶共形场论（CFT）热力学中，除了$(\tilde{T},\tilde{S})$、$(\tilde{Q},\tildeΦ)$、$(\tilde{P},\tildeΨ)$、$(\tilde{\mathcal{P}},\tilde{V})$之外，中心荷$C$及其共轭的化学势$μ$也纳入热力学关系。我们考虑与这五对热力学变量相关的十六种不同系综，将其划分为定容系综与定压系综两类。由于($\tilde{Q},\tilde{P}$)的对称性，我们仅需分别分析定容与定压系综中的五种。在定容系综中，发现固定($\tilde{Q},\tilde{P},\tilde{V},μ$)与($\tildeΦ,\tilde{P},\tilde{V},μ$)的系综存在零级相变。有趣的是，固定($\tildeΦ,\tildeΨ,\tilde{V},C$)的系综在临界势$\tildeΥ_c$以上和以下分别呈现零级与一级相变。在定压系综中，出现了更丰富的结构，其中$μ$的符号对若干系综的相空间有显著影响。对于固定($\tilde{Q},\tilde{P},\tilde{\mathcal{P}},μ$)与($\tildeΦ,\tilde{P},\tilde{\mathcal{P}},μ$)的系综，它们呈现零级、一级与二级相变。对于固定($\tildeΦ,\tildeΨ,\tilde{\mathcal{P}},μ$)的系综，仅存在零级相变。其余未提及的系综最终均未表现出任何相变。这些发现为理解体引力的变动（尤其是宇宙学常数与引力常数的变动）如何转化为CFT中精确的临界现象与更丰富的相结构提供了更深入的见解。
英文摘要
We investigate the holographic dual of the extended bulk thermodynamics of dyonic dilaton AdS black holes by allowing both the cosmological constant and Newton's gravitational constant to vary. In the dual CFT thermodynamics, the central charge $C$ and chemical potential $μ$ as its conjugate enter the thermodynamic relations, in addition to $(\tilde{T},\tilde{S})$, $(\tilde{Q},\tildeΦ)$, $(\tilde{P},\tildeΨ)$, $(\tilde{\mathcal{P}},\tilde{V})$. We consider sixteen different ensembles related to those five pairs of thermodynamic variables which we separate into fixed volume and pressure ensembles. Due to the symmetry on ($\tilde{Q},\tilde{P}$), we only need to analyze five ensembles each in fixed volume and pressure ensembles. In the fixed volume ensembles, it is found that the fixed ($\tilde{Q},\tilde{P},\tilde{V},μ$) and ($\tildeΦ,\tilde{P},\tilde{V},μ$) exhibit a zeroth-order phase transition. Interestingly, the fixed ($\tildeΦ,\tildeΨ,\tilde{V},C$) ensemble shows the zeroth- and first-order phase transitions at above and below critical potential $\tildeΥ_c$, respectively. In the fixed pressure ensembles, it is found that richer structures appear where the sign of $μ$ heavily influences phase space for several ensembles. For fixed ($\tilde{Q},\tilde{P},\tilde{\mathcal{P}},μ$) and ($\tildeΦ,\tilde{P},\tilde{\mathcal{P}},μ$), they show the zeroth-, first-, and second-order phase transitions. For the fixed ($\tildeΦ,\tildeΨ,\tilde{\mathcal{P}},μ$) ensemble, there is only a zeroth-order phase transition occurs. The other ensembles which we do not mention eventually do not show any phase transition. These findings provide deeper insight into how bulk gravitational variations, particularly regarding the cosmological and gravitational constants, translate to exact critical phenomena and richer phase structures within CFT.
