超对称指标对温度和模量的独立性：来自引力的证明
Temperature and Moduli Independence of the Supersymmetric Index from Gravity
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中文总结 AI 辅助
本文证明了在渐近平坦时空中任意 $\mathcal{N} \geq 2$ 四维超引力理论里，每个超对称鞍点对超对称指标的经典贡献与温度和模量无关，且无需吸引子机制，适用于高阶导数修正和多中心黑洞。
中文摘要 AI 辅助
超对称指标给出了黑洞微观态的带符号计数，可以通过具有适当边界条件的引力路径积分直接计算。基于超对称代数的普遍论证，该指标预期与温度无关，并且在远离边缘稳定性墙时，与标量模量的渐近值无关。在引力侧，这一性质已在许多例子中通过显式计算得到验证，但即使在经典层面也缺乏一般性证明。我们填补了这一空白，证明了在渐近平坦时空中任何具有 $\mathcal{N} \geq 2$ 超对称的四维超引力理论中，每个超对称鞍点对指标的经典贡献都与温度和模量无关。该论证仅利用解和Killing旋量方程在无穷远处的行为。因此，该结果在存在任意高阶导数修正以及多中心黑洞构型的情况下依然成立。特别地，模量独立性无需借助依赖于近水平几何的吸引子机制即可得出。
英文摘要
The supersymmetric index, which gives a signed count of the microstates of black holes, can be computed directly from a gravitational path integral with appropriate boundary conditions. From general arguments based on the supersymmetry algebra, the index is expected to be independent of the temperature and, away from walls of marginal stability, of the asymptotic values of the scalar moduli. On the gravity side, this has been verified by explicit computations in many examples, but a general proof is lacking even at the classical level. We fill this gap by showing that in any four-dimensional supergravity theory with $\mathcal{N} \geq 2$ supersymmetry in asymptotically flat space-time, the classical contribution to the index from each supersymmetric saddle is independent of both. The argument uses only the behavior of the solution and of the Killing spinor equations near infinity. The result therefore holds in the presence of arbitrary higher-derivative corrections and for multi-centered black hole configurations. In particular, moduli independence follows without appeal to the attractor mechanism, which relies on the near-horizon geometry.
发表机构
- International Centre for Theoretical Sciences（国际理论科学中心）
机构由 AI 辅助整理，请以论文原文为准。
