Torsionful Killing-Yano Forms under T-Duality: Transformation Conditions and Emergent Isometries

Abstract

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.