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.
Classical and quantum N=2 supersymmetric black holes
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abstract
We use heterotic/type-II prepotentials to study quantum/classical black holes with half the $N=2, D=4$ supersymmetries unbroken. We show that, in the case of heterotic string compactifications, the perturbatively corrected entropy formula is given by the tree-level entropy formula with the tree-level coupling constant replaced by the perturbative coupling constant. In the case of type-II compactifications, we display a new entropy/area formula associated with axion-free black-hole solutions, which depends on the electric and magnetic charges as well as on certain topological data of Calabi--Yau three-folds, namely the intersection numbers, the second Chern class and the Euler number of the three-fold. We show that, for both heterotic and type-II theories, there is the possibility to relax the usual requirement of the non-vanishing of some of the charges and still have a finite entropy.
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Derives analytic α' corrections to the three-charge BMPV black hole geometry and computes its corrected entropy via generalized Wald formula, matching supersymmetric index results.
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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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BMPV black hole at first order in $\alpha'$
Derives analytic α' corrections to the three-charge BMPV black hole geometry and computes its corrected entropy via generalized Wald formula, matching supersymmetric index results.