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.