Quantum gravity constraints on fine structure constant from GUP in braneworlds

Abstract The Generalized Uncertainty Principle (GUP) has been discussed in the thick braneworld scenario. By considering Rydberg atoms this background, we show that spacetime geometry affects Maxwell equations inducing an effective dielectric constant on space. In its turn, corrected Coulomb potential by gravitational interaction yields a deviation 3-dimensional Bohr radius. Then, compute corrections fine structure owing to GUP higher-dimensional spacetime. We also found constraints for deformation parameter $$\beta $$ β and D -dimensional Planck length $$l_{D}$$ l D comparing predicted deviations with recent empirical data of constant. intermediate scale, which principle may be larger than scale. It is conjectured below such scale Quantum Gravity effects should take place.