Abstract
super-Yang-Mills theory on is believed to have a smooth dependence on the circle size . Making small leads to calculable nonperturbative color confinement, mass gap, and string tensions. For finite , the small- low-energy dynamics is described by a three-dimensional effective theory. The large- 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 -winding of the gauge field holonomy, which takes values in . Furthermore, the low-energy description is given by a nontrivial gapless theory, with a space-like Lifshitz scale invariance and operators that pick up anomalous dimensions as is increased. Supersymmetry-breaking deformations leave the long-distance theory scale-invariant, but change the Lifshitz scaling exponent to , and lead to an emergent Lorentz symmetry at small . Adding a small number of fundamental fermion fields leads to matter localized on three-dimensional branes in the emergent four-dimensional theory.
- Received 23 June 2016
DOI:https://doi.org/10.1103/PhysRevD.94.125008
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