Emergent dimensions and branes from large- N confinement

N=1 SU(N) super-Yang-Mills theory on R3×S1 is believed to have a smooth dependence on the circle size L. Making L small leads to calculable nonperturbative color confinement, mass gap, and string tensions. For finite N, the small-L low-energy dynamics is described by a three-dimensional effective theory. The large-N limit, however, reveals surprises: the infrared dual description is in terms of a theory with an emergent fourth dimension, curiously reminiscent of T-duality in string theory. Here, however, the emergent dimension is a lattice, with momenta related to the S1-winding of the gauge field holonomy, which takes values in ZN. Furthermore, the low-energy description is given by a nontrivial gapless theory, with a space-like z=2 Lifshitz scale invariance and operators that pick up anomalous dimensions as L is increased. Supersymmetry-breaking deformations leave the long-distance theory scale-invariant, but change the Lifshitz scaling exponent to z=1, and lead to an emergent Lorentz symmetry at small L. Adding a small number of fundamental fermion fields leads to matter localized on three-dimensional branes in the emergent four-dimensional theory.