Holographic correlators are defined only after choosing a renormalization scheme, i.e. a set of localcovariant counterterms on the regulated boundary. We formalize the space of schemes as an affinebundle over the source manifold (boundary metric and other sources). A renormalization prescriptioninduces a connection on this bundle; changing scheme acts as a gauge transformation shifting theconnection by an exact form. The central claim is that the Weyl anomaly is the resulting curvatureclass: it is precisely the obstruction to global scheme-trivialization compatible with Wess–Zuminoconsistency. We state a theorem identifying the anomaly with curvature in a cohomological quotientand check the construction in AdS3/CFT2, where holographic renormalization reproduces the 2DWeyl anomaly with the standard central charge relation. We then enlarge the source space to includea background U(1) gauge field and isolate a new discovery channel: flat local curvature with nontrivialglobal holonomy along noncontractible loops in source space. Finally, in AdS5 Einstein–Maxwellwith an abelian Chern–Simons term, we compute an explicit nontrivial scheme holonomy for alarge-gauge loop and show it is not removable by finite local gauge-invariant counterterms, thusproducing a concrete torsion/holonomy invariant in holographic renormalization.
SIKX HILTON (Fri,) studied this question.