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Register a new userStrongly Coupled String-inspired Infinite Derivative Non-local Yang-Mills: Diluted Mass Gap
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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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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.
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We show how to consistently renormalize $mathcal{N} = 1$ and $mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $mathcal{N} = 2$ case, this new action is exact at all orders in perturbation theory.
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