• Accepted Paper

Variational approach to infrared divergencies: Applications to black hole action integrals and holographic Wilson loops

M. Arroyo, D. Arteaga, M. Bañados, and A. Faraggi

Phys. Rev. D - Accepted 2 November, 2026

DOI: https://doi.org/10.1103/px2v-g13s

Abstract

Renormalizing the on-shell action variation offers two important advantages over renormalizing the action itself. First, the variation of the action has a universal form in which the bulk contribution vanishes identically. As a result, the renormalization problem is automatically localized at the boundary; no bulk subtractions are required. Second, the variation of the action admits a natural interpretation as a 1-form on functional space. The distinction between exact and non-exact 1-forms provides a clear renormalization prescription. We apply these ideas to the computation of on-shell black hole actions. After presenting the general algorithm, we discuss some examples, including Kerr–Newman, Kerr–Newman–AdS, Taub–NUT, Taub–Bolt, and STU black holes. We also apply the same techniques to the computation of holographic Wilson loops. All results agree with standard results, in particular with holographic renormalization.

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