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

Understand

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.