English

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

Mathematical Physics 2026-07-21 v1 High Energy Physics - Theory

Abstract

We investigate the transformation of Killing-Yano (KY) pp-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 S3S^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.

Keywords

Cite

@article{arxiv.2607.18842,
  title  = {Torsionful Killing-Yano Forms under T-Duality: Transformation Conditions and Emergent Isometries},
  author = {Özgür Kelekçi and Ümit Ertem and Özgür Açık},
  journal= {arXiv preprint arXiv:2607.18842},
  year   = {2026}
}

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40 pages