An exact elliptic superpotential for N=1∗ deformations of finite N=2 gauge theories Original Research Article

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 covariant 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.