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Divergences in the hadronic light-by-light amplitude of the holographic soft-wall model

Josef Leutgeb, Jonas Mager, and Anton Rebhan

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Phys. Rev. D 114, 036033 – Published 31 August, 2026

DOI: https://doi.org/10.1103/4svg-x1ks

Abstract

We use the Wentzel-Kramers-Brillouin approximation to uncover divergences and instances of noncommuting limits in a large class of holographic soft-wall models. We show that the infinite sum over single resonance contributions for a variety of observables involving the Chern-Simons term, such as the vector-vector-axial-vector (VVA) correlator or the hadronic light-by-light tensor, does not converge. These divergences can in some cases (such as the VVA correlator) be traced back to noncommuting limits and avoided by working directly in the five-dimensional setup with bulk-to-boundary propagators. However, the hadronic light-by-light scattering tensor also diverges in the five-dimensional formulation with corresponding Green functions, preventing a correct implementation of the Melnikov-Vainshtein short-distance constraint and even leading to an infinite contribution to the muon g−2. We also discuss modifications of the standard soft-wall model that are able to resolve this issue.

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Phys. Rev. D 114, 036033– Published 31 August, 2026
  • Received 18 December 2025
  • Accepted 14 July 2026
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