1303.4752 (Norbert Bodendorfer et al.)

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

Norbert Bodendorfer, Yasha Neiman

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 extend this result to first-order formulations of gravity, by generalizing a previously proposed boundary term to closed boundaries. As a side effect, we settle the issue of the Holst modification vs. the Nieh-Yan density by demanding a well-defined variational principle. 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. An interpretation and a connection to other recent results is discussed. In particular, we propose that the large-spin limit of loop quantum gravity can be viewed as a high-energy 'transplanckian' regime.

View original: http://arxiv.org/abs/1303.4752