Abstract
We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 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 asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.
Highlights
Conformal invariance in the UV, trans-planckian scale transmutation and dark matter phenomenology, leading to a new directions of UV-completion of 4D Quantum Field Theories, valid and perturbative up to infinite energy scales [55, 56]
We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory
Conformal invariance in the UV, trans-planckian scale transmutation and dark matter phenomenology, leading to a new directions of UV-completion of 4D Quantum Field Theories, valid and perturbative up to infinite energy scales [55, 56].1. Coupled sectors in such a scenario was studied in a scalar field theory case and was found to predict diluted mass gap in the UV, with M determining the corrections to the mass spectrum arising from the infinite sets of higher-derivatives present in the theory
Summary
The idea with this change of variables is to eliminate the exponential non-local factor from the kinetic term just as happens for scalar field theory. Where we added an arbitrary source term jμa that will be useful in the following. This is similar in the way the non-local scalar field theory is formulated. The non-Abelian ghost and gauge-fixing Lagrangians are given by Lghost = −cae−f( )(∂μDμab)cb,. As we have done for the gauge field, the ghost field can be redefined as ca. In this case, we added arbitrary source terms ηa and ηa.
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