We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding the C∗-algebra of the noncommutative torus into an approximately finite algebra. The construction is a rigorous derivation of the recent discretizations of non...

We consider recently-constructed solutions of three dimensional SL(N,R)×SL(N,R) Chern-Simons theories with non-relativistic symmetries. Solutions of the Chern-Simons theories can generically be mapped to solutions of a gravitational theory with a higherspin gauge symmetry. However, we will show that some of the non-relativistic solutions are not equivalent to metric solutions, as this mapping f...

We propose a large N dual of 4d, N = 1 supersymmetric, SU(N) Yang-Mills with adjoint field Φ and arbitrary superpotential W (Φ). The field theory is geometrically engineered via D-branes partially wrapped over certain cycles of a non-trivial Calabi-Yau geometry. The large N , or low-energy, dual arises from a geometric transition of the Calabi-Yau, where the branes have disappeared and have bee...