Revealing Gauge Constraints in LQG-Inspired Yang-Mills Theory

TL;DR

This work shows that gauge symmetry imposes a fundamental constraint on LQG-inspired Planck-scale deformations when embedded into the Standard Model via a covariant dimension-six EFT. By mapping the Levy-Helayël-Neto (LHN) framework into the covariant $\mathcal{O}_{DF}$ and $\mathcal{O}_{F3}$ basis and enforcing non-Abelian Ward identities, the authors demonstrate an on-shell equivalence between kinetic and cubic terms, reducing the apparent freedom of the model. For LHN, the parameters must satisfy $\frac{\theta_3}{\theta_8} = -\frac{1}{2}\left[1 + \theta_7 \left(\frac{\ell_P}{\mathcal{L}}\right)^{2+2\Upsilon}\right] + \mathcal{O}(\ell_P)$, illustrating that gauge consistency selects a constrained subspace rather than an arbitrary parameter set. This framework provides a physically motivated selection principle that tightens the phenomenology of LQG-inspired EFTs and points toward future RG analyses to assess stability under quantum corrections.

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.