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We investigate the non-perturbative regimes in the class of non-Abeliantheories that have been proposed as an ultraviolet completion 4-D Quantum FieldTheory (QFT) generalizing the kinetic energy operators to an infinite series ofhigher-order derivatives inspired by string field theory. We prove that, at thenon-perturbative level, the physical spectrum of the theory is actuallycorrected by the 'infinite number of derivatives' present in the action. Wederive a set of Dyson-Schwinger equations in differential form, for correlationfunctions till two-points, the solution for which are known in the localtheory. We obtain that just like in the local theory, the non-local counterpartdisplays a mass gap, depending also on the mass scale of non-locality, and showthat it is damped in the deep UV reaching asymptotically the conformal limit.We point out some possible implications of our result in particle physics andcosmology and discuss aspects of non-local QCD-like scenarios. We end with somecomments on the infinite-derivative non-local gravity which is quantum gravityapproach to ghost-free, re-normalizable theories of gravity valid upto infinteebergy scales in the UV.

Strongly Coupled String-inspired Infinite Derivative Non-local Yang-Mills: Diluted Mass Gap