On Duality, Legendre Bundles and Deformations
Differential Geometry
2026-04-07 v1
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.
Keywords
Cite
@article{arxiv.2604.04865,
title = {On Duality, Legendre Bundles and Deformations},
author = {N. C. Combe and P. G. Combe and H. K. Nencka},
journal= {arXiv preprint arXiv:2604.04865},
year = {2026}
}