5D Yang-Mills instantons from ABJM Monopoles

TL;DR

This work analyzes M2-branes in a background four-form flux that expand into M5-branes wrapped on a fuzzy S^3, and demonstrates that the fluctuations on the M5/M2 system are captured by five-dimensional MSYM on R^{2,1}×S^2, as derived from both ABJM and D4-brane perspectives. A central result is that eleven-dimensional momentum encoded as magnetic flux in ABJM is mapped directly to instanton flux in the 5D MSYM, providing an explicit M-theory interpretation for these instantons. The paper shows precise agreement between the ABJM fluctuation action and the D4-brane action in the same flux background, extends the analysis to include transverse fluctuations and a twisted supersymmetry on S^2, and outlines non-Abelian generalisations via reducible vacua to obtain U(m) gauge theories on S^2. Overall, it supports the conjecture that instanton numbers encode KK momentum and that 5D MSYM, including instanton sectors, captures the full M2/M5 dynamics in this regime, with implications for the M5-brane description and M-theory dualities.

Abstract

In the presence of a background supergravity flux, N M2-branes will expand via the Myers effect into M5-branes wrapped on a fuzzy three-sphere. In previous work the fluctuations of the M2-branes were shown to be described by the five-dimensional Yang-Mills gauge theory associated to D4-branes. We show that the ABJM prescription for eleven-dimensional momentum in terms of magnetic flux lifts to an instanton flux of the effective five-dimensional Yang-Mills theory on the sphere, giving an M-theory interpretation for these instantons.