  We investigate the non-perturbative degrees of freedom in the class of
non-local Higgs theories that have been proposed as an ultraviolet completion
4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an
infinite series of higher derivatives inspired by string field theory. At the
perturbative level, the degrees of freedom of non-local Higgs are the same of
the local theory. We prove that, at the non-perturbative level, the physical
spectrum of the Higgs mass is actually corrected from the "infinite number of
derivatives" present in the action. The technique we use permits to derive the
set of Dyson-Schwinger equations in differential form. This proves essentially
useful when exact solutions to the local equations are known. We show that all
the formalism of the local theory involving the Dyson-Schwinger approach
extends quite naturally to the non-local case. Using these methods, the
spectrum of non-local theories become accessible and predictable in the
non-perturbative regimes. We calculate the N-point correlation functions and
predict the mass-gap in the spectrum arising purely from the self-interaction
and the non-local scale M. The mass gap generated gets damped in the UV and it
reaches conformal limit. We discuss some implications of our result in particle
physics and cosmology.
