# How Low Can Vacuum Energy Go When Your Fields Are Finite-Dimensional?

## TL;DR

This paper proposes a finite-dimensional quantum field theory framework consistent with holographic bounds, significantly reducing vacuum energy predictions to align with observations.

## Contribution

It introduces a locally finite-dimensional Klein-Gordon field model using generalized Clifford algebras, offering a novel approach to quantum fields under holographic constraints.

## Key findings

- Vacuum energy is greatly suppressed in the finite-dimensional model.
- The construction is essentially unique under the imposed conditions.
- Predicted vacuum energy aligns plausibly with observational data.

## Abstract

According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this paper, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein-Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. We then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.