Renormalized Yang-Mills Energy on Poincar\'e-Einstein Manifolds

We prove that the renormalized Yang-Mills energy on six dimensional Poincar\'e-Einstein spaces can be expressed as the bulk integral of a local, pointwise conformally invariant integrand. We show that the latter agrees with the corresponding anomaly boundary integrand in the seven dimensional r...

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Bibliographic Details
Main Authors Gover, A. R, Latini, E, Waldron, A, Zhang, Y
Format Journal Article
LanguageEnglish
Published 10.09.2024
Subjects
Mathematics - Differential Geometry
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Summary:We prove that the renormalized Yang-Mills energy on six dimensional Poincar\'e-Einstein spaces can be expressed as the bulk integral of a local, pointwise conformally invariant integrand. We show that the latter agrees with the corresponding anomaly boundary integrand in the seven dimensional renormalized Yang-Mills energy. Our methods rely on a generalization of the Chang-Qing-Yang method for computing renormalized volumes of Poincar\'e-Einstein manifolds, as well as known scattering theory results for Schr\"odinger operators with short range potentials.
DOI:10.48550/arxiv.2409.06995