An exact elliptic superpotential for deformations of finite gauge theories - Timothy Hollowood (Nuclear Physics B, 2002)
We study relevant deformations of the N = 2 superconformal theory on the world-volume of N D3 branes at an Ak−1 singularity. In particular, we determine the vacuum structure of the mass-deformed theory with N = 1 supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular co- variant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero-Moser integrable system.