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.
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