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Growth rate conjecture for leading terms in WRT asymptotics

Determine the growth order of the leading terms in the asymptotic expansion of SU(2) Witten–Reshetikhin–Turaev invariants as predicted by the growth rate conjecture, which specifies how the leading power of k in each contribution associated to a Chern–Simons value S is governed by the geometry of the moduli space of flat SU(2) connections.

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Background

The authors highlight, in addition to the asymptotic expansion conjecture, the existence of a growth rate conjecture (referenced as Conjecture 1.2 in prior work) that proposes an explicit description of the order of leading terms in the expansion.

In this paper they obtain bounds consistent with the growth rate conjecture for Seifert fibered homology spheres, but do not resolve the conjecture in general.

References

We highlight that, complementary to Conjecture~\ref{ConjAEC}, there are also the so-called growth rate conjecture [Conjecture~1.2]{Andersen13}, which gives an explicit conjecture for the order of the leading terms of the expansion~eq:AEC, and Witten's semi-classical approximation conjecture (see also Conjecture~1.3 and references in this paper), which gives an explicit formula for the coefficient of the leading terms of the expansion~eq:AEC.

— A proof of Witten's asymptotic expansion conjecture for WRT invariants of Seifert fibered homology spheres (2510.10678 - Andersen et al., 12 Oct 2025) in Introduction, discussion following Conjecture \ref{ConjAEC}