Emergent dimensions and branes from large- N confinement
Emergent dimensions and branes from large- N confinement
复制标题
来自大氮限制的涌现维度和膜
DOI：
10.1103/physrevd.94.125008
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发表时间：
2016
影响因子：
5
通讯作者：
E. Poppitz
中科院分区：
文献类型：
--
作者：
A. Cherman;E. Poppitz
数学上的{N}=1$$SU(N)$超级杨-米尔斯关于S^1的超级杨-米尔斯理论被认为对圆的大小有光滑的依赖关系。使$L$变小会导致可计算的非微扰颜色限制、质量间隙和弦张力。对于有限元N元，用三维有效理论描述了小元L元的低能动力学。然而，巨大的$N$限制揭示了令人惊讶的：红外对偶描述是根据一个具有新兴第四维的理论来描述的，奇怪的是，这让人想起弦理论中的T对偶。然而，这里出现的维度是一个格子，动量与规范场完整的$S^1$缠绕有关，它的值以$\mathbb{Z}_N$为单位。此外，低能描述是由一个非平凡的无隙理论给出的，它具有类空的$z=2$Lifshitz标度不变性和随着$L的增加而拾取反常维度的算符。超对称破缺形变使长程理论保持标度不变，但使Lifshitz标度指数变为$z=1$，并导致在小$L$处出现洛伦兹对称性。在浮现四维理论中，加入少量的基本费米子场导致物质定域在三维膜上。
$\mathcal{N}=1$ $SU(N)$ 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.