Superrenormalizable gauge and gravitational theories

TL;DR

This paper constructs specific nonpolynomial gauge and gravitational theories with infinite derivatives that are superrenormalizable and free of unphysical poles, ensuring consistency and improved convergence in quantum field theory.

Contribution

It explicitly constructs entire functions for nonpolynomial actions that achieve superrenormalizability without introducing unphysical poles, advancing quantum gravity and gauge theory models.

Findings

Theories are perturbatively superrenormalizable.

No unphysical poles are introduced in propagators.

Derived cutting equations confirm absence of unphysical cuts.

Abstract

We investigate 4-dim gauge theories and gravitational theories with nonpolynomial actions containing an infinite series in covariant derivatives of the fields representing the expansion of a transcendental entire function. A class of entire functions is explicitly constructed such that: (i) the theory is perturbatively superrenormalizable; (ii) no (gauge-invariant) unphysical poles are introduced in the propagators. The nonpolynomial nature is essential; it is not possible to simultaneously satisfy (i) and (ii) with any polynomial series in derivatives. Cutting equations are derived verifying the absence of unphysical cuts and the Bogoliubov causality condition within the loop expansion. A generalized KL representation for the 2-point function is obtained exhibiting the consistency of physical positivity with the improved convergence of the propagators. Some physical effects, such as extended bound excitations in the spectrum, are briefly discussed.