Techniques and apparatuses are described for enabling a base station to enable peer-to-peer communication among multiple user equipment (UE) over a mmWave link. The techniques described herein overcome challenges that the multiple UEs might otherwise face in trying to establish peer-to-peer links on their own. By relying on the base station to grant air interface resources for the UE to perform peer-to-peer communications with the UE, the UE can communicate directly with the other UE, independent of links that the UE or the other UE maintains with the base station. Furthermore, reliance on the base station may help the UE and the other UE mitigate interference from other nearby mmWave links that are separate from the peer-to-peer wave link. In addition, by relying on the base station to specify the beam sweeping pattern, beam acquisition by the UE and the other UE may be improved.