IKKT矩阵模型中的模糊球作为黑洞：一项评估
The Fuzzy-Sphere as a Black Hole in the IKKT Matrix Model: An Assessment
- Musashi High School and Junior High School（武藏高中和初中）
- Waseda Junior and Senior High School（早稻田高中和初中）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究在IKKT矩阵模型中引入Myers项计算模糊球背景的单圈热力学，发现熵标度与黑洞不一致，且无固有霍金温度，为未来研究提供定量基准。
AI中文摘要：
黑洞热力学已从BFSS矩阵模型中取得了显著成功的再现，但在密切相关的IKKT矩阵模型中相应的检验一直等待其最近提出的有限温度表述。我们在此框架内研究这一对应关系。引入三次Myers项，我们计算了模糊$S^2$背景的完整单圈热力学——自由能、内能、熵和热容。对于这一特定背景，没有已知的引力对偶，因此我们将这些量与D0和D2黑洞作为最接近的参考点进行比较。在固定Myers耦合下，领头阶熵表现出$O(N^3)$标度，而非传统黑洞特征的$O(N^2)$行为；这一标度失配是我们分析的核心结果。我们进一步发现没有固有的霍金温度——仅有一个特征尺度——以及热容在低温和高温端点均为负值。若固定物理半径，则得到真正的$O(N^2)$标度，因此$N$的幂次依赖于约定而非无歧义的预测——尽管符号和温度尺度的失配在两种情况下均持续存在。这些结果并未确立有限温度IKKT矩阵模型的黑洞解释，而是提供了一个定量基准，未来解析、数值和全息研究可据此进行检验。
英文摘要：
Black-hole thermodynamics has been reproduced with remarkable success from the BFSS matrix model, but the corresponding test in the closely related IKKT matrix model has awaited its recently proposed finite-temperature formulation, within which we investigate this correspondence. Introducing a cubic Myers term, we compute the complete one-loop thermodynamics -- free energy, internal energy, entropy, and heat capacity -- of a fuzzy $S^2$ background, and compare against the D0 and D2 black holes as the closest available reference points, since no gravitational dual is known for this specific background. At fixed Myers coupling, the leading entropy exhibits an $O(N^3)$ scaling rather than the $O(N^2)$ behavior characteristic of conventional black holes. Holding the physical radius fixed instead yields a genuine $O(N^2)$ scaling, showing that the power of $N$ depends on the large-$N$ prescription and is therefore not by itself an unambiguous test of a black-hole interpretation. We further find no intrinsic Hawking temperature -- only a characteristic scale -- and a heat capacity that is negative at low temperature but positive at high temperature. The absence of an intrinsic Hawking temperature, tied to the missing gravitational dual rather than to the choice of large-$N$ prescription, persists in either scaling limit. Rather than establishing a black-hole interpretation of the finite-temperature IKKT matrix model, these results provide a quantitative benchmark against which future analytical, numerical, and holographic investigations can be tested.
