大N约束下的涌现维数和膜世界
Emergent Dimensions and Braneworlds from Large-N Confinement
摘要：
关于$\mathcal{N}=1$的超级杨-米尔斯理论被认为对圆的大小有平滑的依赖性$L$。使$L$小导致可计算的非微扰色禁闭，质量间隙，弦张力。对于有限的$N$，小- $L$低能动力学的三维有效理论描述。然而，大的- $N$极限揭示了令人惊讶的事实：红外对偶描述是根据一个涌现的第四维理论，令人好奇地联想到弦论中的T对偶。然而，在这里，突现维度是一个晶格，动量与规范场完整性的$S^1$ -缠绕有关，它在$\mathbb{Z}_N$中取值。此外，低能量的描述给出了一个非平凡的无隙理论，与空间一样的$z=2$ Lifshitz标度不变性和运营商，拿起异常尺寸为$L$增加。超光速破缺形变使长距离理论保持标度不变，但将Lifshitz标度指数改变为$z=1$，并导致在小的$L$处出现洛伦兹对称性。在四维涌现理论中，加入少量的基本费米子场会导致物质局域在三维膜上。
英文摘要：
$\mathcal{N}=1$ $SU(N)$ 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.
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