One-loop correction to the four-dimensional Planck mass on the supersymmetric M4 x S^2 compactification of Salam-Sezgin supergravity

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Authors: Jeremy Jacala
Cited by: 2

Abstract

We study the one-loop correction to the four-dimensional Newton constant 1/G_N on the supersymmetric Minkowski_4 x S^2 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/G_N is the heat-kernel sum Delta = sum (-1)^F (1/6 - xi_s) dof_s c_1s, which for a mass-degenerate N=1 multiplet collapses to -c_1 Str(dof * xi). Of the five universal curvature couplings, three are sourced heat-kernel results (xi_1/2, xi_1, and the massive Fierz-Pauli value xi_2); xi_3/2 rests on a structural Stueckelberg derivation, and xi_0 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/G_N 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 An appendix isolates the regularization error of the superseded preprint (doi:10.5281/zenodo.19160221): a polynomial-split spectral regularization silently drops a finite term, exactly -c^2/2 per curvature-shifted tower (mu = u^2 - 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charged monopole-tower value is -1/40 (not +1/10; there is no sign flip), and the corrected 13-sector sum of the superseded preprint is -2/15 (not 43/15). This paper supersedes the withdrawn preprint at doi:10.5281/zenodo.19160221.

Fields of Study & Subjects

Black Holes and Theoretical Physics Noncommutative and Quantum Gravity Theories Particle physics theoretical and experimental studies

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
10 June 2026
Language
EN