Classical BPS M5-Brane on the Plane-Wave Background

Abstract We consider the bosonic theory for a single M5-brane on the plane-wave background and derive a family of Bogomol’nyi–Prasad–Sommerfield (BPS) solutions with nonzero components of the angular momentum. By explicit construction of a BPS solution, we find the solution describes an ellipsoidal five-brane rotating without changing its shape. The methodology developed in this paper is expected to provide a strategy for obtaining the BPS solutions that correspond to a BPS sector in the dual gauge theory, such as the Berenstein–Maldacena–Nastase (BMN) matrix model.