  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.
