Revealing Gauge Constraints in LQG-Inspired Yang-Mills Theory

TL;DR

This paper investigates how gauge symmetry constraints shape the low-energy effects of Loop Quantum Gravity within the Standard Model, revealing that parameter choices in LQG-inspired models are physically restricted by gauge invariance.

Contribution

It demonstrates that gauge symmetry imposes strict conditions on LQG-inspired effective theories, deriving specific parameter relations to ensure consistency with the Standard Model.

Findings

LQG effects must satisfy gauge invariance constraints

Derived a fundamental on-shell equivalence between kinetic and interaction terms

Identified algebraic relations among parameters in LQG-inspired models

Abstract

The consistent embedding of Loop Quantum Gravity (LQG) effects within the Standard Model requires a rigorous understanding of how Planck-scale deformations manifest at low energies. While phenomenological approaches often introduce canonical deformations with multiple free parameters to capture these effects, the physical requirement of gauge symmetry in the framework of a covariant Effective Field Theory (EFT) imposes strict conditions on the allowed interaction structure. In this paper, we demonstrate that these conditions act as physical selection rules for admissible quantum gravity models. By applying non-Abelian Ward identities and a covariant operator mapping to the dimension-six operator basis, we derive a fundamental on-shell equivalence between kinetic and cubic interaction terms. As a paradigmatic application, we show that the Levy-Helayel-Neto (LHN) framework, a candidate effective description of LQG, satisfies this physical requirement only when its parameters obey the specific algebraic relation: theta_3 / theta_8 = -1/2 * [ 1 + theta_7 * (ell_P / L)^(2 + 2 Upsilon) ] + O(ell_P). It must be highlighted that this result advances the physical understanding of LQG phenomenology by revealing that the apparent freedom in defining the Hamiltonian is illusory; the parameters are bound by the necessity of preserving the gauge structure of the Standard Model.