arXiv 2501.033122025-01hep-th

存在空间圆时的弦星相

Phases of String Stars in the Presence of a Spatial Circle

Jinwei Chu

备注：: 26 pages, 13 figures, Additional results added to the $d=6$ case

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AI总结：

本文利用HP有效场理论研究欧几里得时空中弦星的相变，发现四次修正能在不同维度下解除质量简并、逆转温度变化方向，并引发燕尾型相图及反常稳定性。

摘要：

在弦理论中，当黑洞的Hawking温度接近Hagedorn温度时，预期它们会转变为弦星。我们在欧几里得时空$\mathbb{R}^d\times\mathbb{S}_τ^1\times\mathbb{S}_z^1$中研究了弦星及其相变。使用Horowitz-Polchinski (HP)有效场理论，我们发现了$d=2$时的全新解。均匀弦星表现出标度对称性，导致其向非均匀解转变的过程不存在临界点。对于$d=4$，我们证明了对有效作用的四次修正解除了均匀弦星的质量简并。在$d=5$时，我们发现随着非均匀性增加，四次项变得显著（而高阶项仍可忽略）并逆转了温度变化的方向，导致正则系综中出现燕尾型相图。将四次修正的EFT扩展到$d=6$，我们发现具有小非均匀性的弦星在微正则系综中占主导地位，但在正则系综中不占主导，这与$d=5$的情况类似。然而，在微正则系综中，当空间圆大于（小于）临界尺寸时，均匀弦星表现出反常的稳定（不稳定）性。

英文摘要：

In string theory, black holes are expected to transition into string stars as their Hawking temperatures approach the Hagedorn temperature. We study string stars and their phase transitions in the Euclidean spacetime $\mathbb{R}^d\times\mathbb{S}_τ^1\times\mathbb{S}_z^1$. Using the Horowitz-Polchinski (HP) effective field theory, we discover novel solutions for $d=2$. The uniform string star exhibits a scaling symmetry that results in the absence of a critical point for its transition into the non-uniform solution. For $d=4$, we show that quartic corrections to the effective action resolve the mass degeneracy of uniform string stars. At $d=5$, we find that as non-uniformity increases, the quartic terms become significant (while higher-order terms remain negligible) and reverse the direction of temperature variation, leading to a swallowtail-type phase diagram in the canonical ensemble. Extending the quartic-corrected EFT to $d=6$, we find that string stars with small non-uniformity dominate the microcanonical ensemble but not the canonical ensemble, similar to the $d=5$ case. However, in the microcanonical ensemble, the uniform string star is anomalously (un)stable when the spatial circle is larger (smaller) than the critical size.

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