Challenging Gauge/Gravity Duality: A Potential-Centric Perspective

Abstract

The AdS/CFT correspondence posits a holographic equivalence between a gravitational theory in Anti-de Sitter (AdS) spacetime and a conformal field theory (CFT) on its boundary, linked by gauge-invariant quantities like field strengths F_{\mu\nu} and fluxes \Phi. This paper examines that link, drawing on my prior analysis of the Aharonov-Bohm (AB) effect, where such quantities exhibit nonlocality, discontinuity, and incompleteness. I demonstrate that gauge potentials A_\mu in the Lorenz gauge—not their invariant derivatives—mediate the AB effect’s local, continuous dynamics, a reality extending to gravitational fields g_{\mu\nu} as substantival entities. In AdS/CFT, the CFT’s reduction of bulk A_\mu and g_{\mu\nu} to gauge-invariant imprints fails to reflect this ontology, a flaw so fundamental that it excludes exact gauge/gravity duality—neither standard mappings nor reformulations suffice. A new mathematical proof formalizes this: the bulk’s diffeomorphism freedom cannot correspond to the boundary’s gauge freedoms, Abelian or non-Abelian, under this reality. This critique spans the gauge/gravity paradigm broadly, from AdS/CFT to holographic QCD, where symmetry invisibility obscures bulk physics. While duality’s successes in black hole thermodynamics and strongly coupled systems highlight its utility, I suggest these reflect approximations within specific regimes, not a full equivalence. I propose a shift toward a framework prioritizing A_\mu and g_{\mu\nu}’s roles, with gravitational AB effects in AdS as a testing ground. This work seeks to enrich holography’s dialogue, advancing a potential-centric view for quantum gravity