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arXiv · 2603.10819

Generalised Complex and Spinor Relations

Thomas C. De Fraja·Vincenzo Emilio Marotta·Richard J. Szabo
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Abstract

Courant algebroid relations are used to define notions of relations between Dirac structures and spinors. It is shown under which circumstances a spinor relation gives a Courant algebroid relation and how it descends to a relation between Dirac structures. A converse to this result is proved: a T-duality relation induces a spinor relation that links the Dirac generating operators defining T-dual Courant algebroids, generalising the isomorphism of twisted cohomology associated with topological T-duality. We introduce the notion of relation between generalised complex structures and characterise their reduction. We also define relations between generalised K\"ahler structures, and rephrase them in terms of bi-Hermitian structures which induce T-duality relations between $\mathcal{N}=(2,2)$ supersymmetric sigma-models. We prove existence results for T-dual structures, and demonstrate compatibility of T-duality relations with Type II supergravity equations.

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Thomas C. De Fraja, Vincenzo Emilio Marotta, Richard J. Szabo. 2026-03-11. Generalised Complex and Spinor Relations. https://arxiv.org/abs/2603.10819

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