Asymptotic occurrence of the torsion term in the Turaev–Viro invariant

Determine whether the term expressed by the appropriately normalized absolute square of adjoint Reidemeister torsion, together with the associated peripheral and geometric factors identified in Theorem 1.3, appears in the asymptotic expansion of the Turaev–Viro invariant.

Background

The paper proves a geometric one-loop formula for Turaev–Viro-type state-integral invariants associated with cusped hyperbolic 3-manifolds. This formula relates Gram determinants, decorated edge lengths, cone-angle Jacobians, and the appropriately normalized absolute square of adjoint Reidemeister torsion.

The authors note that the same explicit torsion-related expression appears in the asymptotic expansion of the meromorphic 3D-index after applying their one-loop formula. They leave unresolved whether an analogous term occurs in the asymptotic expansion of the classical Turaev–Viro invariant.