Time Delays of Strings in D-particle Backgrounds and Vacuum Refractive Indices

TL;DR

This paper investigates how open strings interacting with D-particles in brane world scenarios cause energy-dependent time delays, especially for photons, which could impact cosmic photon observations and help distinguish between different string scale models.

Contribution

It introduces novel selection rules for causal time delays in string-D-particle interactions and explores their implications for vacuum refractive indices and astrophysical photon phenomenology.

Findings

Time delays are proportional to the energy of incident particles.

Large delays occur mainly for excitations in the Cartan subalgebra of the SM.

Astrophysical observations can constrain or falsify low-string-scale models.

Abstract

Using standard techniques in string/D-brane scattering amplitude computations, we evaluate the scattering of open strings off D-particles in brane world scenarios. The D-particles are viewed as D3 branes wrapped up around three cycles, and their embedding in brane worlds constitutes a case of intersecting branes, among which strings are stretched, representing various types of excitations of the Standard Model (SM) particles in the low-energy limit. Our analysis, reveals interesting and novel selection rules for the resulting causal time delays, proportional to the energy of the incident matter state, from the processes of splitting, capture and re-emission of the latter by the D-particles. In particular, we show that there are relatively large time delays only for excitations that belong to the Cartan subalgebra of the SM gauge group, which notably includes photons. We discuss the possible relevance of these results to the models of space time foam predicting a non-trivial vacuum refractive index for photons and the associated cosmic \gamma-ray phenomenology. In particular, we demonstrate how low-string-scale models can be falsified already in this context, by current astrophysical observations of cosmic photons, and how such observations serve as a way to discriminate low- from high-string scale models.