Perfect discretizations as a gateway to one-loop partition functions for 4D gravity
arXiv:2112.03307 · doi:10.1007/JHEP05(2022)172
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.
22 pages
References in corpus (6)
- Tensor renormalization group approach to 2D classical lattice models
- Perfect discretization of reparametrization invariant path integrals
- One-loop partition function of three-dimensional flat gravity
- Spacetime could be simultaneously continuous and discrete in the same way that information can
- Coarse graining free theories with gauge symmetries: the linearized case
- Discretization independence implies non-locality in 4D discrete quantum gravity