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arXiv · 2604.04865

On Duality, Legendre Bundles and Deformations

N. C. Combe·P. G. Combe·H. K. Nencka
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Abstract

We introduce the Legendre bundle, a geometric structure encoding the essential duality of dually flat (Hessian) manifolds, and demonstrate that both exponential families in information geometry and a natural class of quantum field theories -- which we term Hessian QFTs -- arise as distinct realisations of this single framework. The Legendre bundle is shown to carry a canonical para-K\"ahler structure.

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N. C. Combe, P. G. Combe, H. K. Nencka. 2026-04-06. On Duality, Legendre Bundles and Deformations. https://arxiv.org/abs/2604.04865

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