The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories

TL;DR

This paper investigates the fuzzy S^2 structure emerging in M2-M5 systems within ABJM membrane theories, revealing a novel realization of the fuzzy 2-sphere using bifundamental scalars and connecting it to D4-brane physics.

Contribution

It demonstrates that fluctuations in ABJM M2-M5 solutions approach functions on a fuzzy 2-sphere, providing new insights into the geometric structure of these systems and their string theory interpretations.

Findings

Fluctuations approach functions on S^2, not S^3.

Large N limit yields a U(1) Yang-Mills theory on R^{2,1} x S^2.

Fuzzy 3-sphere differs from ABJM solutions, indicating distinct geometric structures.

Abstract

We analyse the fluctuations of the ground-state/funnel solutions proposed to describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter ABJM theory of multiple membranes. We show that in the large N limit the fluctuations approach the space of functions on the 2-sphere rather than the naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in the context of Matrix Theories, which uses bifundamental instead of adjoint scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory on R^{2,1} x S^2 is recovered at large N, which is consistent with a single D4-brane interpretation in Type IIA string theory. This is as expected at large k, where the semiclassical analysis is valid. Several aspects of the fluctuation analysis, the ground-state/funnel solutions and the mass-deformed/pure ABJM equations can be understood in terms of a discrete noncommutative realisation of the Hopf fibration. We discuss the implications for the possibility of finding an M2-brane worldvolume derivation of the classical S^3 geometry of the M2-M5 system. Using a rewriting of the equations of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show them to be different.