A proof of The Radial Limit Conjecture for Costantino--Geer--Patureau-Mirand Quantum invariants

TL;DR

This paper proves the Radial Limit Conjecture for quantum invariants of certain three-manifolds, showing that an average of GPPV invariants has a resurgent asymptotic expansion with the CGP invariant as the leading term.

Contribution

It provides the first proof of the Radial Limit Conjecture for GPPV invariants, establishing a deep connection between quantum invariants and asymptotic analysis.

Findings

Integral representation of GPPV invariants for negative definite plumbed 3-manifolds

Resurgent asymptotic expansion of the average of GPPV invariants

Leading term matches the Costantino--Geer--Patureau-Mirand invariant

Abstract

For a negative definite plumbed three-manifold, we give an integral representation of the appropriate average of the GPPV invariants of Gukov--Pei--Putrov--Vafa, which implies that this average admits a resurgent asymptotic expansion, the leading term of which is the Costantino--Geer--Patureau-Mirand invariant of the three-manifold. This proves a conjecture of Costantino--Gukov--Putrov.