Emergent Dimensions and Braneworlds from Large-N Confinement

TL;DR

This paper explores how large-N super-Yang-Mills theory on a circle exhibits an emergent fourth dimension with Lifshitz scale invariance, revealing novel non-perturbative phenomena and brane-like matter localization.

Contribution

It uncovers the emergence of a fourth dimension and Lifshitz scaling in large-N super-Yang-Mills, linking gauge theory dynamics to higher-dimensional and string-inspired concepts.

Findings

Emergent fourth dimension from gauge holonomy momenta

Lifshitz $z=2$ scale invariance in low-energy limit

Matter localized on branes in the emergent dimension

Abstract

$\mathcal{N}=1$ $SU(N)$ 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.