虚action、自旋泡沫渐近和圈量子引力的transplanck区
Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity
摘要：
最近注意到，具有York-Gibbons-Hawking边界项的壳层上的Einstein-Hilbert作用量具有虚部，虚部与边界法线为零的余维2表面的面积成比例。我们讨论了这一结果的扩展到一阶公式的重力。作为一个副作用，我们解决了霍尔斯特修改与Nieh-Yan密度的问题，需要一个变分原理与适当的边界条件。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量。事实证明，自旋泡沫的有效作用确实具有正确的虚部，但前提是在量子计算之后将Barbero-Immirzi参数设置为+/- i。我们指出，这一有效的行动和最近的黑洞状态计数计算在同一限制之间的协议。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“transplanck”机制。
英文摘要：
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 vs. 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 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.
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