First limits on the very-high energy gamma-ray afterglow emission of a fast radio burst: H.E.S.S. observations of FRB 150418

Aims: Following the detection of the fast radio burst FRB150418 by the SUPERB project at the Parkes radio telescope, we aim to search for very-high energy gamma-ray afterglow emission. Methods: Follow-up observations in the very-high energy gamma-ray domain were obtained with the H.E.S.S. imaging atmospheric Cherenkov telescope system within 14.5 hours of the radio burst. Results: The obtained 1.4 hours of gamma-ray observations are presented and discussed. At the 99 % C.L. we obtained an integral upper limit on the gamma-ray flux of (E>350 GeV) < 1.33 x 10^-8 m^-2s^-1. Differential flux upper limits as function of the photon energy were derived and used to constrain the intrinsic high-energy afterglow emission of FRB 150418. Conclusions: No hints for high-energy afterglow emission of FRB 150418 were found. Taking absorption on the extragalactic background light into account and assuming a distance of z = 0.492 based on radio and optical counterpart studies and consistent with the FRB dispersion, we constrain the gamma-ray luminosity at 1 TeV to L < 5.1 x 10^47 erg/s at 99% C.L.