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arXiv · 1303.4752

Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity

Norbert Bodendorfer·Yasha Neiman
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Abstract

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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Norbert Bodendorfer, Yasha Neiman. 2013-09-12. Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity. https://doi.org/10.1088/0264-9381%2F30%2F19%2F195018

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