On general ultraviolet properties of a class of confining propagators

TL;DR

This paper demonstrates that confining propagators with complex poles do not alter the ultraviolet behavior of quantum field theories, ensuring their renormalizability across various models including supersymmetric cases.

Contribution

It proves that confining propagators of the Gribov type do not introduce new ultraviolet divergences, maintaining renormalizability in a broad class of theories.

Findings

Confining propagators do not affect ultraviolet divergences.

Renormalizability is preserved in models with confining propagators.

The results hold for supersymmetric theories like ${\cal N}=1$ Super Yang-Mills.

Abstract

We study the ultraviolet properties of theories whose fundamental fields display a confining, Gribov-type, propagator. These are propagators that exhibit complex poles and violate positivity, thus precluding a physical propagating particle interpretation. We show that the properties of this type of confining propagators do not change the ultraviolet behavior of the theory, in the sense that no new ultraviolet primitive divergences are generated, thus securing the renormalizability of these confining theories. We illustrate these properties by studying a variety of models, including bosonic and fermionic confined degrees of freedom. The more intricate case of Super Yang-Mills with ${\cal N} =1$ supersymmetries in the Wess-Zumino gauge is taken as example in order to prove these statements to all orders by means of the algebraic renormalization set up.