On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant an...

We construct a variety of supersymmetric gauge theories on a spatial lattice, including N = 4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at the desired continuum limit in these examples.

We review some of the uses of Whitham hierarchies in the context of the theory of the prepotential in N = 2 supersymmetric gauge theories. We focus on the structure of the contact terms in the twisted topological theory, and on the connection between Whitham hierarchies and the u-plane integrals for higher rank gauge groups, trying to put together the different approaches involved in this conne...