Ground States of S-duality Twisted N=4 Super Yang-Mills Theory

We study the low-energy limit of a compactification of N=4 U(n) super Yang-Mills theory on $S^1$ with boundary conditions modified by an S-duality and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the $T^2$ compactification of this 2+1D theory by identifying a dual weakly coupled type-IIA background. The Hilbert space of normalizable ground states is finite-dimensional and appears to exhibit a rich structure of sectors. We identify most of them with Hilbert spaces of Chern-Simons theory (with appropriate gauge groups and levels). We also discuss a realization of a related twisted compactification in terms of the (2,0)-theory, where the recent solution by Gaiotto and Witten of the boundary conditions describing D3-branes ending on a (p,q) 5-brane plays a crucial role.