论文标题
$ W_3 $更高自旋全息图中充电的时刻
Charged Moments in $W_3$ Higher Spin Holography
论文作者
论文摘要
我们考虑$ sl（3，\ mathbb {r}）中的带电矩，以及具有$ W_3 $对称性的双重二维形成性场理论。对于真空状态和单个纠缠间隔，我们表明，保形场理论的$ W_3 $代数诱导纠缠$ W_3 $代数在纠缠间隔中符合量子状态。代数包含一个自旋3模块化电荷，该电荷用模块化的哈密顿量通勤。降低的密度矩阵的特征是模块化能量和模块化电荷，因此我们对带电矩的定义也与这些保守量有关。我们通过计算模块化电荷运算符的相应连接的相关函数，在化学势中最高至四分之一的相关相关函数，在自旋3模块化化学电位上对带电矩的对数进行了扰动。此方法提供了无需使用带电的扭转场而无需使用带电的时刻的访问。我们的结果匹配了从$ sl（3，\ mathbb {r}）$更高的自旋重力中获得的带电拓扑黑洞图片获得的带电力矩的已知结果。由于我们的充电时刻不再是化学潜力的高斯，因此我们得出的结论是，双$ W_3 $共形的场理论必须以纠缠纠缠的优点分解为大型$ C $扩展中的领先订单。
We consider the charged moments in $SL(3,\mathbb{R})$ higher spin holography, as well as in the dual two-dimensional conformal field theory with $W_3$ symmetry. For the vacuum state and a single entangling interval, we show that the $W_3$ algebra of the conformal field theory induces an entanglement $W_3$ algebra acting on the quantum state in the entangling interval. The algebra contains a spin 3 modular charge which commutes with the modular Hamiltonian. The reduced density matrix is characterized by the modular energy and modular charge, hence our definition of the charged moments is also with respect to these conserved quantities. We evaluate the logarithm of the charged moments perturbatively in the spin 3 modular chemical potential, by computing the corresponding connected correlation functions of the modular charge operator up to quartic order in the chemical potential. This method provides access to the charged moments without using charged twist fields. Our result matches known results for the charged moment obtained from the charged topological black hole picture in $SL(3,\mathbb{R})$ higher spin gravity. Since our charged moments are not Gaussian in the chemical potential any longer, we conclude that the dual $W_3$ conformal field theories must feature breakdown of equipartition of entanglement to leading order in the large $c$ expansion.
