Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.
The Symplectic Structure of N=2 Supergravity and its Central Extension
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abstract
We report on the formulation of $N=2$ $D=4$ supergravity coupled to $n_V$ abelian vector multiplets in presence of electric and magnetic charges. General formulae for the (moduli dependent) electric and magnetic charges for the $n_V+1$ gauge fields are given which reflect the symplectic structure of the underlying special geometry. The specification to Type IIB strings compactified on Calabi-Yau manifolds, with gauge group $U(1)^{h_{21}+1}$ is given.
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Axionic string tensions define vector fields on moduli space that split into mutually orthogonal subsets with one decoupling from gravity, and their Laplacian relates to divergent moduli space curvature.
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Optimal paths across potentials on scalar field space
Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.
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Gravity Decoupling and Axionic Shift Symmetries
Axionic string tensions define vector fields on moduli space that split into mutually orthogonal subsets with one decoupling from gravity, and their Laplacian relates to divergent moduli space curvature.