A Nonperturbative Test of M2-Brane Theory

TL;DR

The paper tests the ABJM description of multiple M2-branes by analyzing nonperturbative monopole instantons in the $U(N)_1\times U(N)_2$ Chern-Simons-matter theory and matching their four-derivative and eight-fermion vertices to bulk M-theory/D0-brane exchanges. It demonstrates that each monopole instanton carries eight fermionic zero modes and yields nonperturbative corrections that scale as $(u_1/u_2)^{k|m|}$, with $m$ labeling the instanton sector, and that the same structure emerges from eleven-dimensional supergravity and its IIA reduction. The M-theory bulk calculations reproduce the field-theoretic vertices, including their vev-dependence, providing a nonperturbative corroboration of ABJM as the worldvolume theory of multiple M2-branes on $\mathbb{C}^4/\mathbb{Z}_k$. The results strengthen the holographic link between ABJM and M2-brane dynamics, showing quantitative agreement across the field theory and bulk descriptions, including D0-brane/D2-brane exchanges in the IIA picture. Overall, the work offers a concrete nonperturbative bridge between ABJM dynamics and M-theory, clarifying the role of monopole instantons in the M2-brane context.

Abstract

We discuss non-perturbative effects in the ABJM model due to monopole instantons. We begin by constructing the instanton solutions in the $U(2)\times U(2)$ model, explicitly, and computing the Euclidean action. The Wick-rotated Lagrangian is complex and its BPS monopole instantons are found to be a delicate version of the usual 't Hooft-Polyakov monopole solutions. They are generically 1/3 BPS but become 1/2 BPS at special locus in the moduli space of two M2-branes, yet each instanton carries eight fermionic zero modes, regardless of the vacuum choice. The low energy effective action induced by monopole instantons are quartic order in derivatives. The resulting vertices are nonperturbative in $1/k$, as expected, but are rational functions of the vacuum moduli. We also analyze the system of two M2-branes in the supergravity framework and compute the higher order interactions via 11-dimensional supergraviton exchange. The comparison of the two shows that the instanton vertices are precisely reproduced by this M2-brane picture, supporting the proposal that the ABJM model describes multiple M2-branes.

Figures (1)

• Figure 1: (a) Two M2-branes placed in the $\mathbb{C}/\mathbb{Z}_k$ subspace of the cone $\mathbb{C}^4/\mathbb{Z}_k$. (b) The covering space view of the same configuration.