A Nonperturbative Test of M2-Brane Theory

TL;DR

This paper investigates nonperturbative effects in the ABJM model caused by monopole instantons, constructing explicit solutions and comparing them with supergravity predictions to support the M2-brane theory.

Contribution

It provides explicit monopole instanton solutions in the ABJM model and demonstrates their agreement with supergravity calculations, confirming the M2-brane interpretation.

Findings

Instanton solutions are 1/3 BPS, becoming 1/2 BPS at special loci.

Instanton vertices match supergravity interactions, supporting the M2-brane description.

Instanton effects are nonperturbative in 1/k and depend rationally on vacuum moduli.

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.