规范D=5矢量多重态视界上的第二个转动Killing场，以及变模黑洞环的禁则
A second rotational Killing field on gauged $D=5$ vector-multiplet horizons, and a no-go for varying-moduli black rings
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中文总结 AI 辅助
该研究分析规范D=5超引力耦合矢量多重态的超对称近视界几何，证明紧致无边界视界上存在第二个独立转动Killing场，导出变模黑洞环的禁则，明确不同模条件下的视界几何分类。
中文摘要 AI 辅助
我们研究规范D=5超引力耦合矢量多重态的超对称近视界几何，其截面$\mathcal{S}$的正则转动Killing矢量$\tilde{V}$非零，且未假设转动对称性，也未对由Killing旋子构造的标架退化的集合做任何限定。在紧致连通无边界的$\mathcal{S}$上，始终存在一个独立于$\tilde{V}$的第二个转动Killing场，它是整个$\mathcal{S}$的等距变换。在模变化区域，该场为$$U_i=\parallel\eta_-\parallel^2\big(\alpha Z_i-\epsilon_{ijk}Z^ju^k\big), \qquad u_i=\Phi P_i-h_i,$$是视界数据的多项式，因此处处光滑；在模恒定区域，视界局部齐次。这些结果的唯一额外假设是超势$\Phi=\chi V_IX^I$处处非零，弱于早期文献中假设的标量势非负性。两个子分支由$K=Q_{IJ}C^IC^J$分隔，在极小理论中$K\equiv0$，可还原Grover、Gutowski、Papadopoulos和Sabra的结果；其他区域$K>0$，且$\alpha$要么恒为零要么处处非零。在紧致$\mathcal{S}$上分别存在$K\equiv0$、$P\equiv0$和$P\not\equiv0$的情况。模恒定的结论是Kunduri和Lucietti的局部几何，而非假设。$\alpha\not\equiv0$的变模情况给出一个共形一维$T^2$作用，其轨道空间为闭区间，故$\mathcal{S}$为$S^3$、透镜空间或$S^1\times S^2$；后一种情况被两个全局第一积分排除，一个是新的$\alpha\parallel\eta_-\parallel^4$，另一个是已知的常旋子模。因此，$\alpha\not\equiv0$时不存在变模超对称$AdS_5$黑洞环；$S^1\times S^2$窗口仅在模恒定或$\alpha\equiv0$时存在。
英文摘要
We study supersymmetric near-horizon geometries of gauged $D=5$ supergravity coupled to vector multiplets, on the branch where the canonical rotational Killing vector $\tilde V$ of the cross-section ${\cal S}$ is non-vanishing. No rotational symmetry is assumed, and nothing about the set where the frame built from the Killing spinors degenerates. On a compact connected ${\cal S}$ without boundary a second rotational Killing field, independent of $\tilde V$, always exists and is an isometry of all of ${\cal S}$. Where the moduli vary it is $$ U_i=\parallelη_-\parallel^2\big(αZ_i-ε_{ijk}Z^ju^k\big) , \qquad u_i=ΦP_i-h_i , $$ a polynomial in the horizon data, hence smooth everywhere; where the moduli are constant the horizon is locally homogeneous. The only further hypothesis for these results is that the superpotential $Φ=χV_IX^I$ is nowhere zero --- weaker than the non-negativity of the scalar potential assumed in the earlier literature. The two sub-branches are separated by $K=Q_{IJ}C^IC^J$, which vanishes exactly in the minimal theory: $K\equiv0$ recovers the result of Grover, Gutowski, Papadopoulos and Sabra, while elsewhere $K>0$ and $α$ is either identically zero or nowhere zero. Each of $K\equiv0$, $P\equiv0$ and $P\not\equiv0$ occurs on compact ${\cal S}$. Constant moduli return the local geometries of Kunduri and Lucietti as a conclusion, not an ansatz. Varying moduli with $α\not\equiv0$ give a cohomogeneity-one $T^2$ action whose orbit space is a closed interval, so ${\cal S}$ is $S^3$, a lens space or $S^1\times S^2$; the last is excluded by two global first integrals, a new one, $α\parallelη_-\parallel^4$, and the constant spinor norm already known. A varying-moduli supersymmetric $AdS_5$ black ring therefore cannot exist with $α\not\equiv0$; the $S^1\times S^2$ window survives only at constant moduli or at $α\equiv0$.
