Semiclassical Analysis of M2-brane in AdS_4 x S^7 / Z_k

TL;DR

This paper analyzes semiclassical fluctuations of an M2-brane in AdS_4 x S^7/Z_k, revealing supermultiplet structures and their implications for Wilson loop deformations in a holographic context.

Contribution

It provides a detailed semiclassical analysis of M2-brane fluctuations in AdS_4 x S^7/Z_k, connecting them to supermultiplets and boundary deformations.

Findings

Fluctuations form N=1 supermultiplets on AdS_2

Set of fluctuations invariant under SO(8)

Insights into Wilson loop operator deformations

Abstract

We start from the classical action describing a single M2-brane on AdS_4 x S^7/ Z_k and consider semiclassical fluctuaitions around a static, 1/2 BPS configuration whose shape is AdS_2 x S^1. The internal manifold S^7/ Z_k is described as a U(1) fibration over CP^3 and the static configuration is wrapped on the U(1) fiber. Then the configuration is reduced to an AdS_2 world-sheet of type IIA string on AdS_4 x CP^3 through the Kaluza-Klein reduction on the S^1. It is shown that the fluctuations form an infinite set of N=1 supermultiplets on AdS_2, for k=1,2. The set is invariant under SO(8) which may be consistent with N=8 supersymmetry on AdS_2. We discuss the behavior of the fluctuations around the boundary of AdS_2 and its relation to deformations of Wilson loop operator.