Toward a Proof of Montonen-Olive Duality via Multiple M2-branes

TL;DR

This paper derives 4D N=4 supersymmetric Yang-Mills theory from a 3D Chern-Simons-matter theory involving M2-branes, providing evidence for Montonen-Olive duality through M-theory insights.

Contribution

It presents a novel derivation of 4D N=4 SYM from M2-branes and demonstrates part of the SL(2,Z) duality, advancing the proof of Montonen-Olive duality.

Findings

Multiple equivalent 4D theories related by T-transformations

Partial realization of SL(2,Z) duality via M2-brane action

Connection between orbifold M2-branes and 4D gauge theories

Abstract

We derive 4-dimensional N=4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group U(N)^{2n}. The latter describes M2-branes probing an orbifold where a torus emerges in a scaling limit. It is expected that the SL(2, Z) duality of the 4-dimensional Yang-Mills theory will be shown in M-theory point of view since it is trivially realized as modular transformations of the torus. Indeed, starting from one single Chern-Simons-matter theory, we find infinitely many equivalent 4-dimensional theories differing up to T-transformation of the SL(2, Z) redefinition of the gauge coupling tau=theta/2pi + 4pi i/g^2 and a parity transformation in 4 dimensions. Although S-transformation can not be shown in our work, it is important that a part of the SL(2, Z) transformation is realized via the M2-brane action. Thus we think our work can be a step toward a proof of Montonen-Olive duality via M2-branes.