Spikes and spines in 4D Lorentzian simplicial quantum gravity

TL;DR

This paper investigates spike and spine configurations in 4D Lorentzian quantum Regge calculus, showing that expectation values of bulk lengths are finite and exploring asymptotic regimes with large edges, which simplify the amplitudes and suggest a dimensional reduction possibly relevant for holography.

Contribution

It introduces new asymptotic regimes for Regge amplitudes where some edges are large, ensuring finiteness of length expectations and revealing a potential holographic dimensional reduction.

Findings

Expectation values of bulk lengths are finite.

New asymptotic regimes simplify amplitudes.

Geometric interpretation involves dimensional reduction.

Abstract

Simplicial approaches to quantum gravity such as quantum Regge calculus and spin foams include configurations where bulk edges can become arbitrarily large while the boundary edges are kept small. Spikes and spines are prime examples for such configurations. They pose a significant challenge for a desired continuum limit, for which the average lengths of edges ought to become very small. Here we investigate spike and spine configurations in four-dimensional Lorentzian quantum Regge calculus. We find that the expectation values of arbitrary powers of the bulk length are finite. To that end, we explore new types of asymptotic regimes for the Regge amplitudes, in which some of the edges are much larger than the remaining ones. The amplitudes simplify considerably in such asymptotic regimes and the geometric interpretation of the resulting expressions involves a dimensional reduction, which might have applications to holography.