Toward a Proof of Montonen-Olive Duality via Multiple M2-branes
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.
Cite
@article{arxiv.0809.2137,
title = {Toward a Proof of Montonen-Olive Duality via Multiple M2-branes},
author = {Koji Hashimoto and Ta-Sheng Tai and Seiji Terashima},
journal= {arXiv preprint arXiv:0809.2137},
year = {2009}
}
Comments
28 pages, 2 figures, JHEP style; v2: references added; v3: published version. Abstract improved, Appendix A added forderiving the fermionic sector