Emergent dimensions and branes from large-N confinement
Abstract
N =1 S U (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.
- Publication:
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Physical Review D
- Pub Date:
- December 2016
- DOI:
- 10.1103/PhysRevD.94.125008
- arXiv:
- arXiv:1606.01902
- Bibcode:
- 2016PhRvD..94l5008C
- Keywords:
-
- High Energy Physics - Theory;
- High Energy Physics - Lattice;
- High Energy Physics - Phenomenology
- E-Print:
- v3: published version, containing further improvements to exposition