On Effective Action of Multiple M5-branes and ABJM Action

TL;DR

This work develops a concrete ABJM-based route toward the effective action of multiple M5-branes by expanding around a classical M5-brane solution that uplifts a flat D4 with magnetic flux. The authors derive a D4-like action with a spacetime-dependent gauge coupling $\frac{1}{g_{YM}^2}=\frac{k^2}{16\pi^3\Theta v\sqrt{r^2+r'^2}}$, and show how the geometry of $\mathbb{C}^4/\mathbb{Z}_k$ induces this non-uniform coupling via a five-dimensional Yang-Mills–type theory. They perform a systematic expansion of the bosonic potential to two commutators, map the real and imaginary parts of the scalars, and obtain the fluctuation action around the M5-brane solution, highlighting the emergence of a nontrivial Nambu-Poisson structure. The study also points to the necessity of incorporating monopole operators to include non-zero Kaluza–Klein modes and to fully realize M5-brane dynamics, outlining directions for future work and refinements.

Abstract

We calculate the fluctuations from the classical multiple M5-brane solution of ABJM action which we found in the previous paper. We obtain D4-brane-like action but the gauge coupling constant depends on the spacetime coordinate. This is consistent with the expected properties of M5-brane action, although we will need to take into account the monopole operators in order to fully understand M5-branes. We also see that the Nambu-Poisson bracket is hidden in the solution.