  We investigate the non-perturbative regimes in the class of non-Abelian
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-order derivatives inspired by string field theory. We prove that, at the
non-perturbative level, the physical spectrum of the theory is actually
corrected by the 'infinite number of derivatives' present in the action. We
derive a set of Dyson-Schwinger equations in differential form, for correlation
functions till two-points, the solution for which are known in the local
theory. We obtain that just like in the local theory, the non-local counterpart
displays a mass gap, depending also on the mass scale of non-locality, and show
that it is damped in the deep UV reaching asymptotically the conformal limit.
We point out some possible implications of our result in particle physics and
cosmology and discuss aspects of non-local QCD-like scenarios. We end with some
comments on the infinite-derivative non-local gravity which is quantum gravity
approach to ghost-free, re-normalizable theories of gravity valid upto infinte
ebergy scales in the UV.
