High Energy Physics - Theory
[Submitted on 6 Jun 2016 (v1), last revised 15 Nov 2016 (this version, v3)]
Title:Emergent Dimensions and Braneworlds from Large-N Confinement
View PDFAbstract:$\mathcal{N}=1$ $SU(N)$ super-Yang-Mills theory on $\mathbb{R}^3\times S^1$ is believed to have a smooth dependence on the circle size $L$. Making $L$ small leads to calculable non-perturbative 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 $S^1$-winding of the gauge field holonomy, which takes values in $\mathbb{Z}_N$. Furthermore, the low-energy description is given by a non-trivial 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.
Submission history
From: Aleksey Cherman [view email][v1] Mon, 6 Jun 2016 20:00:07 UTC (165 KB)
[v2] Fri, 21 Oct 2016 19:11:08 UTC (170 KB)
[v3] Tue, 15 Nov 2016 17:33:42 UTC (171 KB)
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