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June 12, 2026Open Access

One-loop correction to the four-dimensional Planck mass on the supersymmetric M4 x S² compactification of Salam-Sezgin supergravity

Key Points

The aim is to analyze the one-loop correction to the four-dimensional Newton constant in a specific supergravity model.
Studied the supersymmetric Minkowski_4 x S^2 vacuum of six-dimensional N=(1,0) supergravity.
Calculated the one-loop logarithmic renormalization of 1/G_N using heat-kernel sums.
Handled contributions from the Kaluza-Klein tower in the compactification process.
The contribution to 1/G_N from the Kaluza-Klein tower is Delta = -1/10, driven by massive supergravity multiplets.
Identities were corrected showing values for neutral and charged monopole towers differ from previous work.
The corrected 13-sector sum yielded -2/15, resolving numerical discrepancies.

Abstract

We study the one-loop correction to the four-dimensional Newton constant 1/GN on the supersymmetric Minkowski₄ x S² vacuum of six-dimensional N= (1, 0) gauged Einstein-Maxwell (Salam-Sezgin) supergravity, and reduce it to a compact closed form. Because the q=1 monopole vacuum is supersymmetric, the calculation is intrinsically supersymmetric: it runs over the four-dimensional N=1 Kaluza-Klein supermultiplets, bosons and fermions together, in the two-derivative theory obtained as the M -> infinity limit of the Pang-Pope-Sezgin spectrum. The one-loop logarithmic renormalization of 1/GN is the heat-kernel sum Delta = sum (-1) F (1/6 - xiₛ) dofₛ c₁s, which for a mass-degenerate N=1 multiplet collapses to -c₁ Str (dof * xi). Of the five universal curvature couplings, three are sourced heat-kernel results (xi₁/2, xi₁, and the massive Fierz-Pauli value xi₂) ; xi₃/2 rests on a structural Stueckelberg derivation, and xi₀ on Einstein-frame N=1 supergravity matching. Conditional on these inputs and a stated matching assumption, the massive vector multiplets cancel while the massive supergravity multiplet does not, and the Kaluza-Klein tower contribution to 1/GN is Delta = -1/10, carried entirely by the massive supergravity tower. This is a compactification-threshold contribution, distinct from the ordinary four-dimensional running of the massless sector; it carries no target value and no numerology. An appendix isolates the regularization error of the superseded preprint (doi: 10. 5281/zenodo. 19160221): a polynomial-split spectral regularization silently drops a finite term, exactly -c²/2 per curvature-shifted tower (mu = u² - c). Worked examples: the genuine neutral-tower value is -1/15 (not -17/480), the genuine charged monopole-tower value is -1/40 (not +1/10; there is no sign flip), and the corrected 13-sector sum of the superseded preprint is -2/15 (not 43/15). This paper supersedes the withdrawn preprint at doi: 10. 5281/zenodo. 19160221.

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