Perfect discretizations as a gateway to one-loop partition functions for 4D gravity

TL;DR

This paper constructs perfect discretizations for 4D linearized gravity, enabling straightforward calculation of one-loop quantum corrections and highlighting the importance of boundary gauge modes in quantum gravity.

Contribution

First construction of perfect discretizations for four-dimensional linearized gravity, facilitating quantum corrections and boundary mode analysis.

Findings

Perfect discretizations preserve continuum symmetries in 4D gravity.

One-loop quantum corrections can be derived from these discretizations.

Boundary gauge modes significantly influence quantum corrections.

Abstract

Lattice actions and amplitudes that perfectly mirror continuum physics are known as perfect discretizations. Such perfect discretizations naturally preserve the symmetries of the continuum. This is a key concern for general relativity, where diffeomorphism symmetry and dynamics are deeply connected, and diffeomorphisms play a crucial role in quantization. In this work we construct for the first time a perfect discretizations for four-dimensional linearized gravity. We show how the perfect discretizations do lead to a straightforward construction of the one-loop quantum corrections for manifolds with boundary. This will also illustrate, that for manifolds with boundaries, gauge modes that affect the boundary, need to be taken into account for the computation of the one-loop correction. This work provides therefore an evaluation of the boundary action for the diffeomorphism modes for a general class of backgrounds.