Non-commutative moduli spaces, dielectric tori and T-duality

We review and extend recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N=4 super Yang–Mills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds some light on the dynamics of the D-brane bubbles. Different regions of moduli space are associated with D5-branes of various topologies; singularities in the moduli space are associated with topology change. T-duality on toroidal topologies maps between mirror string realizations of the field theory.