Geometric entropy and edge modes of the electromagnetic field
Geometric entropy and edge modes of the electromagnetic field
复制标题
电磁场的几何熵和边缘模式
DOI：
10.1103/physrevd.94.104053
复制
发表时间：
2015
影响因子：
5
通讯作者：
Aron C. Wall
中科院分区：
文献类型：
--
作者：
William Donnelly;Aron C. Wall
通过将麦克斯韦理论约化到二维基流形上，计算了弯曲时空中该理论的真空纠缠熵.利用二维对偶性，我们将电磁场的几何熵表示为标量场、恒定的电通量和磁通量以及接触项的塔的熵，接触项的首阶发散由Kabat发现。完整的接触项采取一个负标量自由度的形式，仅限于纠缠表面。我们表明，几何熵同意纠缠熵的统计定义，包括边缘模式：经典的解决方案，由它们的边界值上的纠缠表面。这解决了纠缠熵中接触项的统计解释的长期难题。我们讨论了黑洞热力学和牛顿常数的重整化这个负项的影响。
We calculate the vacuum entanglement entropy of Maxwell theory in a class of curved spacetimes by Kaluza-Klein reduction of the theory onto a two-dimensional base manifold. Using two-dimensional duality, we express the geometric entropy of the electromagnetic field as the entropy of a tower of scalar fields, constant electric and magnetic fluxes, and a contact term, whose leading-order divergence was discovered by Kabat. The complete contact term takes the form of one negative scalar degree of freedom confined to the entangling surface. We show that the geometric entropy agrees with a statistical definition of entanglement entropy that includes edge modes: classical solutions determined by their boundary values on the entangling surface. This resolves a long-standing puzzle about the statistical interpretation of the contact term in the entanglement entropy. We discuss the implications of this negative term for black hole thermodynamics and the renormalization of Newton's constant.