Computing renormalized curvature integrals on Poincar\'e-Einstein manifolds

Autor:	Case, Jeffrey S., Khaitan, Ayush, Lin, Yueh-Ju, Tyrrell, Aaron J., Yuan, Wei
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry High Energy Physics - Theory
Druh dokumentu:	Working Paper
Popis:	We describe a general procedure for computing renormalized curvature integrals on Poincar\'e-Einstein manifolds. In particular, we explain the connection between the Gauss-Bonnet-type formulas of Albin and Chang-Qing-Yang for the renormalized volume, and explicitly identify a scalar conformal invariant in the latter formula. Our approach constructs scalar conformal invariants that are divergences at any Einstein manifold; these imply that the scalar invariant in the Chang-Qing-Yang formula is not unique in dimension at least eight. Our procedure also produces explicit conformally invariant Gauss-Bonnet-type formulas for compact Einstein manifolds. Comment: Improved introduction to better highlight some applications; 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.11319 Zobrazit plný text záznamu View this record from Arxiv