Constraints on the String T-Duality Propagator from the Hydrogen Atom

We investigated the implications of string theory in the high-precision regime of quantum mechanics. In particular, we examined a quantum field theoretical propagator which was derived from string theory when compactified at the T-duality self-dual radius and which is closely related to the path integral duality. Our focus was on the hydrogen ground state energy and the 1 S 1 / 2 − 2 S 1 / 2 transition frequency, as they are the most precisely explored properties of the hydrogen atom. The T-duality propagator alters the photon field dynamics leading to a modified Coulomb potential. Thus, our study is complementary to investigations where the electron evolution is modified, as in studies of a minimal length in the context of the generalized uncertainty principle. The first manifestation of the T-duality propagator arises at fourth order in the fine-structure constant, including a logarithmic term. For the first time, constraints on the underlying parameter, the zero-point length, are presented. They reach down to 3.9 × 10 − 19 m and are in full agreement with previous studies on black holes.