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arXiv · 2409.06995

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

A. R. Gover·E. Latini·A. Waldron·Y. Zhang
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Abstract

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.

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A. R. Gover, E. Latini, A. Waldron, Y. Zhang. 2024-09-11. Renormalized Yang-Mills Energy on Poincar\'e-Einstein Manifolds. https://arxiv.org/abs/2409.06995

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