What question did this study set out to answer?

The aim is to develop a scalar theory that aligns with the Radial Acceleration Relation under conformal invariance in AdS5 geometry.

April 13, 2026Open Access

The Radial Acceleration Relation from AdS5 Conformal Symmetry

Key Points

The aim is to develop a scalar theory that aligns with the Radial Acceleration Relation under conformal invariance in AdS5 geometry.
Formulated a screened scalar theory based on conformal invariance in five-dimensional AdS space.
Derived inner and outer limits analytically while verifying interpolation numerically.
Tested model against a dataset of 3,391 measurements from 175 SPARC galaxies.
Successfully reproduced the Radial Acceleration Relation in the weak-field regime of disk galaxies.
Demonstrated analytical and numerical consistency of the model with empirical galaxy data.

Abstract

This preprint presents an effective screened scalar theory whose coupling function is uniquely determined by a conformal invariance condition in five-dimensional Anti-de Sitter (AdS5) geometry. The resulting framework reproduces the observed Radial Acceleration Relation (RAR) in the weak-field regime of disk galaxies. The logarithmic coupling is selected uniquely under continuity and symmetry assumptions. The inner and outer limits are derived analytically, while the interpolation between them is numerically verified against the full field equation. The model is tested against 3,391 measurements across 175 SPARC galaxies. The manuscript explicitly distinguishes rigorous derivations, physically motivated assumptions, numerical verification, and empirical inputs. This version represents the complete preprint prior to journal submission.

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