Semiclassical Analysis of M2-brane in AdS4 x S7 / Zk
Abstract
We start from the classical action describing a single M2-brane on AdS4 x S7/ Zk and consider semiclassical fluctuaitions around a static, 1/2 BPS configuration whose shape is AdS2 x S1. The internal manifold S7/ Zk is described as a U(1) fibration over CP3 and the static configuration is wrapped on the U(1) fiber. Then the configuration is reduced to an AdS2 world-sheet of type IIA string on AdS4 x CP3 through the Kaluza-Klein reduction on the S1. It is shown that the fluctuations form an infinite set of N=1 supermultiplets on AdS2, for k=1,2. The set is invariant under SO(8) which may be consistent with N=8 supersymmetry on AdS2. We discuss the behavior of the fluctuations around the boundary of AdS2 and its relation to deformations of Wilson loop operator.