T对偶下的扭结Killing-Yano形式：变换条件与涌现等距性
Torsionful Killing-Yano Forms under T-Duality: Transformation Conditions and Emergent Isometries
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中文总结 AI 辅助
研究非平凡三形式挠率下阿贝尔T对偶中Killing-Yano p形式变换，利用特定联络和规则推导出变换定律，应用于多例子并分析结果，还给出T对偶几何中涌现Killing 1形式的相关解释。
中文摘要 AI 辅助
我们研究了在存在非平凡三形式挠率的阿贝尔T对偶下Killing-Yano（KY）p形式的变换。利用一个与挠率兼容的度规联络和T对偶的Buscher规则，在明确的匹配假设下，我们推导出适用于任意度数KY形式的紧凑、无坐标变换定律。特别地，我们表明当一个Killing 1形式的横向分量与等距方向无关时，它会被直接对偶映射保留，对偶圆分量由一个标量校正方程确定。然后将该框架应用于几个例子，包括\(S^3\)的霍普夫T对偶、史瓦西时空以及具有精确NS-NS挠率的纳皮-维滕平面波，我们在其中明确分析了变换后的Killing-Yano形式。最后，我们给出了T对偶几何中涌现Killing 1形式的广义几何和双场理论解释，展示了它们如何从原始对偶框架中的广义Killing数据产生。
英文摘要
We investigate the transformation of Killing-Yano (KY) $p$-forms under Abelian T-duality in the presence of a non-trivial three-form torsion. Using a torsionful, metric-compatible connection and the Buscher rules of T-duality, we derive compact, coordinate-free transformation laws applicable to KY forms of arbitrary degree under explicit matching assumptions. In particular, we show that a Killing 1-form is preserved by the direct duality map whenever its transverse components are independent of the isometry direction, with the dual circle component determined by a scalar correction equation. The framework is then applied to several examples, including the Hopf T-dual of $S^3$, Schwarzschild spacetime, and the Nappi-Witten plane wave with exact NS-NS torsion, where we analyze the transformed Killing-Yano forms explicitly. Finally, we give a generalized-geometric and double-field-theoretic interpretation of emergent Killing 1-forms in the T-dual geometry, showing how they arise from generalized Killing data in the original duality frame.
