论文标题
库仑分支的全息纠缠熵
Holographic Entanglement Entropy of the Coulomb Branch
论文作者
论文摘要
我们计算球形区域的纠缠熵（EE），$（3+1）$ - 尺寸$ \ Mathcal {n} = 4 $ supersymmetric $ su（n）$ yang-mills理论在propical paphraphical the Stondical op proce d3-branes in $ ads_5 \ dims_5 \ tims s^5 $中所描述的状态。我们通过概括从探针brane作用计算EE的方法来做到这一点，而无需确定探针的后反应。在库仑分支上，$ su（n）$损坏至$ su（n-1）\ times u（1）$，我们发现EE单调随着球体半径的增加而单调减少，与$ a-a-a-a $ theorem一致。 $ su（n-1）$筛选的对称代表性的EE也单调减少，尽管没有已知的物理原理需要这一点。已经提出了一个从$ su（n-1）\ times u（1）$内部分开的球形孤子，将$ su（n）$分开，以模拟极端的黑洞。但是，我们发现在索利顿半径处的球体的EE不会随表面积扩展。对于筛选的Wilson线和Soliton，大半径的EE均由位置依赖性W玻璃体质量描述为短距离截止。我们对Lagrangian和应力能量张量的EE的全息效果和一分点功能表明，在很大距离处，Soliton在基本表示的直接产品中看起来像Wilson线。
We compute entanglement entropy (EE) of a spherical region in $(3+1)$-dimensional $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory in states described holographically by probe D3-branes in $AdS_5 \times S^5$. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe's back-reaction. On the Coulomb branch with $SU(N)$ broken to $SU(N-1)\times U(1)$, we find the EE monotonically decreases as the sphere's radius increases, consistent with the $a$-theorem. The EE of a symmetric-representation Wilson line screened in $SU(N-1)$ also monotonically decreases, although no known physical principle requires this. A spherical soliton separating $SU(N)$ inside from $SU(N-1)\times U(1)$ outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton's radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations.
