What question did this study set out to answer?

To explore torsion invariants in a framework utilizing 2-group sources within a holographic context.

January 25, 2026Open Access

2-Group Holonomy in Holographic Scheme Bundles: A Torsion Invariant from Discrete Inflow

Key Points

To explore torsion invariants in a framework utilizing 2-group sources within a holographic context.
Extended counter term-bundle and connection framework to 4D.
Incorporated nonabelian 0-form connections and ZN 1-form backgrounds.
Constructed affine bundles of local covariant counterterms over an enlarged source space.
Exhibited a loop in source space with nontrivial holonomy.
Observed a locally flat loop with nontrivial Nth-root-of-unity holonomy.
Demonstrated that the torsion phase arises from a discrete inflow functional that cannot be eliminated.
Presented an explicit example in 4 dimensions yielding nontrivial ±1 holonomy.

Abstract

We extend the counter term-bundle/ connection framework to background 2-group sources in a4D boundary setting.The source space includes a nonabelian 0-form background connection A fora compact group G and a ZN1-form background B coupled by a Postnikov class β ∈ H3 (BG,ZN),enforced by the constraint δB=β(A). We construct the affine bundle of local covariantcounterterms over the enlarged source space and exhibit a concrete loop γ in source space thatis locally flat (Ω|γ=0) but carries a nontrivial Nth-root-of-unityholonomy.This torsion phaseis generated by a discretein flow functional Sinflow ∝ B ∪ β (A) and cannot be removed by anyfinite local gauge-invariant boundary counterterm preserving the Postnikov constraint. We workout an explicit example with d=4,N=2, and X4=S1×RP3, obtaining a nontrivial ±1holonomy.

2-Group Holonomy in Holographic Scheme Bundles: A Torsion Invariant from Discrete Inflow

Key Points

Abstract

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