  We suggest that M-theory could be non-perturbatively equivalent to a local
quantum field theory. More precisely, we present a ``renormalizable'' gauge
theory in eleven dimensions, and show that it exhibits various properties
expected of quantum M-theory, most notably the holographic principle of
't~Hooft and Susskind. The theory also satisfies Mach's principle: A
macroscopically large space-time (and the inertia of low-energy excitations) is
generated by a large number of ``partons'' in the microscopic theory. We argue
that at low energies in large eleven dimensions, the theory should be
effectively described by eleven-dimensional supergravity. This effective
description breaks down at much lower energies than naively expected, precisely
when the system saturates the Bekenstein bound on energy density. We show that
the number of partons scales like the area of the surface surrounding the
system, and discuss how this holographic reduction of degrees of freedom
affects the cosmological constant problem. We propose the holographic field
theory as a candidate for a covariant, non-perturbative formulation of quantum
M-theory.
