Multibump solutions for a class of critical fractional Choquard equation

In this paper, we investigate the existence of multibump solutions for the critical fractional Choquard equation [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] is the Riesz potential with [Formula: see text], and [Formula: see text] is the critical exponent with respect to the Hardy–Littlewood–Sobolev inequality, the potential [Formula: see text] is periodic in one of its variables and permits a global maxima with a fast decay rate near the maximum point. By combining the variational gluing method and a penalization technique, we prove that for any [Formula: see text], there exist infinitely many [Formula: see text]-bump solutions concentrating near the maxima of [Formula: see text], these solutions exhibit polynomial decay at infinity.