Imaginary action, spinfoam asymptotics and the ‘transplanckian’ regime of loop quantum gravity
Imaginary action, spinfoam asymptotics and the ‘transplanckian’ regime of loop quantum gravity
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想象的作用、自旋泡沫渐近学和圈量子引力的“跨普朗克”体系
DOI：
10.1088/0264-9381/30/19/195018
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发表时间：
2013
影响因子：
3.5
通讯作者：
Yasha Neiman
中科院分区：
文献类型：
--
作者：
N. Bodendorfer;Yasha Neiman
最近有人注意到，具有York-Gibbons-Hawking边界项的壳上爱因斯坦-希尔伯特作用量有一个虚部，与边界法线变为零的余维-2曲面的面积成正比。我们讨论了这一结果在一阶引力公式中的推广。作为一个副作用，我们通过要求一个带有适当边界条件的变分原理来解决Holst修正对Nieh-yan密度的问题。然后，我们开始寻找洛伦兹EPRL/FK自旋泡沫的大自旋4-单形极限中的虚作用。结果表明，自旋泡沫的有效作用确实具有正确的虚部，但前提是量子计算后将Barbero-Immirzi参数γ设置为±i。我们指出，这一有效的行动与最近的一次黑洞状态计数计算在相同的极限下是一致的。最后，我们提出圈量子引力的大自旋极限可以看作是一个高能的“跨普朗克”区域。
It was recently noted that the on-shell Einstein–Hilbert action with York–Gibbons–Hawking boundary term has an imaginary part, proportional to the area of the codimension-2 surfaces on which the boundary normal becomes null. We discuss the extension of this result to first-order formulations of gravity. As a side effect, we settle the issue of the Holst modification versus the Nieh–Yan density by demanding a variational principle with suitable boundary conditions. We then set out to find the imaginary action in the large-spin 4-simplex limit of the Lorentzian EPRL/FK spinfoam. It turns out that the spinfoam’s effective action indeed has the correct imaginary part, but only if the Barbero–Immirzi parameter γ is set to ±i after the quantum calculation. We point out an agreement between this effective action and a recent black hole state-counting calculation in the same limit. Finally, we propose that the large-spin limit of loop quantum gravity can be viewed as a high-energy ‘transplanckian’ regime.
影响因子：
3.5
作者：
J. Barrett;R. J. Dowdall;W. Fairbairn;F. Hellmann;R. Pereira
通讯作者：
J. Barrett;R. J. Dowdall;W. Fairbairn;F. Hellmann;R. Pereira