On the Structural Uniqueness of Quantum Gravity: Gauge-Holographic Reduction of Ambiguity in the BV Formalism

Abstract

We formalize the heuristic systemic principle defining physical determinism as the ratio of redundancy to organizing constraints into a rigorous framework of quantum gauge theories. Within the Batalin-Vilkovisky (BV) formalism, we investigate a comprehensive effective action of quantum gravity defined on a manifold with a conformal boundary, incorporating the Standard Model fields, higher-order stringy corrections, and supersymmetric terms. We prove that the simultaneous cancellation of internal gauge anomalies and boundary ultraviolet divergences uniquely fixes the bulk coupling coefficients and restricts the matter spectrum. Any violation of these structural constraints relegates the effective field theory to the Swampland. Furthermore, we demonstrate that this gauge-holographic constraint naturally addresses the cosmological constant problem by linking the vacuum energy density to the infrared geometric scale of the boundary.