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

TL;DR

This paper extends the understanding of imaginary actions in gravity to first-order formulations, analyzes the spinfoam effective action in the large-spin limit, and suggests this limit as a transplanckian regime in loop quantum gravity.

Contribution

It demonstrates the presence of the imaginary part of the action in first-order gravity and connects it with spinfoam asymptotics, proposing a transplanckian regime in loop quantum gravity.

Findings

Effective spinfoam action has correct imaginary part with Barbero-Immirzi parameter set to +/- i.

Agreement between spinfoam effective action and black hole state-counting calculations.

Large-spin limit of loop quantum gravity can be viewed as a high-energy transplanckian regime.

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.