Fuzzy Ring from M2-brane Giant Torus

TL;DR

This work addresses how angular momentum can be endowed to dielectric branes in AdS4 backgrounds by constructing spinning dual M2 giant gravitons in $AdS_4\times S^7/Z_k$ and showing their world-volumes become toroidal. Via a $Z_k$ orbifold, these M-theory solutions reduce to spinning dielectric D2-branes in $AdS_4\times CP^3$, revealing a concrete mechanism where flux-induced Poynting vectors drive topology change from a sphere to a torus and potentially to a ring. The authors derive explicit BPS equations and provide analytic solutions that describe two topologies: a giant spike and a giant torus, with enhanced supersymmetry in special parameter choices. They also discuss the interpretation in ABJM via dual operators, the emergence of fuzzy rings, and the tantalizing possibility of supersymmetric black rings in $AdS_4$ from these bound states. Overall, the paper expands the catalog of BPS objects in $AdS_4$ and links M-theory giants, dielectric D2-branes, and ABJM operators through precise topological and flux-based mechanisms.

Abstract

We construct spinning dual M2 giant gravitons in AdS_4 x S^7, which generically become 1/16 BPS states, and show that their world-volumes become torii. By taking an orbifold, we obtain spinning dielectric D2-brane configurations in AdS_4 x CP^3 dual to specific BPS operators in ABJM theory. This reveals a novel mechanism how to give an angular momentum to a dielectric D2-brane. We also find that when its angular momentum in the AdS_4 becomes large, it approaches to a ring-like object. Our result might suggest an existence of supersymmetric black rings in the AdS_4 background. We will also discuss dual giant gravitons in AdS_4 x CP^3.

Figures (3)

• Figure 1: If we collides closed strings with a fuzzy sphere (or a dielectric D2-brane), it should begin spinning. To give a non-vanishing angular momentum, we need fundamental strings which connect between the North Pole and the South Pole. By regarding the total system as a bound state of a D2-brane, D0-branes and F-strings, its world-volume becomes a torus. In this paper we will present an exact profile of this configuration by solving the BPS equation.
• Figure 2: The giant-spike solution described in the three dimensional space $(r,\theta,\varphi)$ (we assumed $|w|=10$ and $A=3$). This corresponds to the sign $\eta w<0$. We multiplied the factor 10 with the horizontal coordinates.
• Figure 3: The giant-torus solution corresponding to the sign $\eta w>0$ (we assumed $|w|=10$ and $A=0.8$).