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arXiv 2202.08290hep-thgr-qc
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改进的Wald形式和混合Chern-Simons项双音黑弦的第一定律

Improved Wald formalism and First Law of Dyonic Black Strings with Mixed Chern-Simons Terms

Liang Ma, Yi Pang, H. Lu

备注：
Latex, 27 pages, adding discussions on attractor mechanism, to appear in JHEP
发表信息：
JHEP10(2022)142
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摘要：

本文研究了带首阶$α'$修正的K3上紧化的IIA型弦论中带有线性动量的双子黑弦的热力学第一定律。低能有效作用量包含$-2B_{(2)}\wedge {\rm tr}(R(Γ_\pm)\wedge R(Γ_\pm))$形式的混合Chern-Simons项，其相当于$2H_{(3)}\wedge \mathrm{CS}_{(3)}(Γ_\pm)$直至全导数。我们发现，Wald熵公式的天真应用导致两个不同的答案与混合陈-西蒙斯条款的两个配方。令人惊讶的是，他们都不满足热力学热力学第一定律的其他保守电荷计算明确使用标准方法。我们解决这个问题，仔细评估在无限远和地平线上的全部无穷小哈密顿量，包括从成比例的Killing矢量的贡献，这是在地平线上的非零和必不可少的建立第一定律。我们发现与$-2B_{(2)}\wedge {\rm tr}(R(Γ_\pm)\wedge R(Γ_\pm))$相关的无穷小哈密顿量需要通过增加一个封闭但不精确的项来改进，当弦不携带磁荷或线性动量时，该项消失。因此，混合陈-西蒙斯项的两种公式都产生相同的熵结果，但与瓦尔德熵公式不一致。在极端黑弦的情况下，我们也将我们的结果与森的方法得到的结果进行了对比。

英文摘要：

We study the first law of thermodynamics of dyonic black strings carrying a linear momentum in type IIA string theory compactified on K3 with leading order $α'$ corrections. The low energy effective action contains mixed Chern-Simons terms of the form $-2B_{(2)}\wedge {\rm tr}(R(Γ_\pm)\wedge R(Γ_\pm))$ which is equivalent to $2H_{(3)}\wedge \mathrm{CS}_{(3)}(Γ_\pm)$ up to a total derivative. We find that the naive application of Wald entropy formula leads to two different answers associated with the two formulations of the mixed Chern-Simons terms. Surprisingly, neither of them satisfies the first law of thermodynamics for other conserved charges computed unambiguously using the standard methods. We resolve this problem by carefully evaluating the full infinitesimal Hamiltonian at both infinity and horizon, including contributions from terms proportional to the Killing vector which turn out to be nonvanishing on the horizon and indispensable to establish the first law. We find that the infinitesimal Hamiltionian associated with $-2B_{(2)}\wedge {\rm tr}(R(Γ_\pm)\wedge R(Γ_\pm))$ requires an improvement via adding a closed but non-exact term, which vanishes when the string does not carry either the magnetic charge or linear momentum. Consequently, both formulations of the mixed Chern-Simons terms yield the same result of the entropy that however does not agree with the Wald entropy formula. In the case of extremal black strings, we also contrast our result with the one obtained from Sen's approach.

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