论文标题
局部重力淬火的纠缠熵
Entanglement entropy of local gravitational quenches
论文作者
论文摘要
我们研究由整数旋转$ s \ leq 2 $ in 4 $ dimensions创建的本地兴奋状态的rényi/纠缠端的时间依赖性。对于旋转0，1这些状态的特征是给定宽度的局部能量密度，这些宽度以光速作为球形波传播。对于自旋2情况，在没有局部规格不变应力张量的情况下，我们使用Kretschmann标量探测这些状态，并表明它们代表以光速传播的局部曲率密度。我们考虑使用这些激发的半空间的降低密度矩阵，并开发出一种方便的量规选择，以评估这些淬灭进入半区域时rényi/纠缠熵的时间依赖性。在所有情况下，纠缠熵在$ \ log 2 $中的时间增长和饱和。在极限上，这些激发的宽度趋于零，增长取决于$ 2S+1 $ $多项式的订单，以距离co-Dimension-2纠缠表面和时间的距离比。可以根据$（2）_T \ times so（2）_l $对称性来组织对应于该场产生的淬灭的多项式，可以通过co-Dimension 2纠缠的表面保留。对于在此对称性下以标量为标量的字段，$ 2S+1 $多项式的顺序完全由自旋确定。
We study the time dependence of Rényi/entanglement entropies of locally excited states created by fields with integer spins $s \leq 2$ in $4$ dimensions. For spins 0, 1 these states are characterised by localised energy densities of a given width which travel as a spherical wave at the speed of light. For the spin 2 case, in the absence of a local gauge invariant stress tensor, we probe these states with the Kretschmann scalar and show they represent localised curvature densities which travel at the speed of light. We consider the reduced density matrix of the half space with these excitations and develop methods which include a convenient gauge choice to evaluate the time dependence of Rényi/entanglement entropies as these quenches enter the half region. In all cases, the entanglement entropy grows in time and saturates at $\log 2 $. In the limit, the width of these excitations tends to zero, the growth is determined by order $2s+1$ polynomials in the ratio of the distance from the co-dimension-2 entangling surface and time. The polynomials corresponding to quenches created by the fields can be organised in terms of their representations under the $SO(2)_T\times SO(2)_L$ symmetry preserved by the presence of the co-dimension 2 entangling surface. For fields transforming as scalars under this symmetry, the order $2s+1$ polynomial is completely determined by the spin.
