Nahm sums, stability and the colored Jones polynomial

Abstract

Nahm sums are $q$-series of a special hypergeometric type that appear in character formulas in Conformal Field Theory, and give rise to elements of the Bloch group, and have interesting modularity properties. In our paper, we show how Nahm sums arise naturally in Quantum Knot Theory, namely we prove the stability of the coefficients of the colored Jones polynomial of an alternating link and present a Nahm sum formula for the resulting power series, defined in terms of a reduced diagram of the alternating link. The Nahm sum formula comes with a computer implementation, illustrated in numerous examples of proven or conjectural identities among $q$-series.

Latex, 57 pages and 111 figures

References in corpus (5)

• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial
• Walks Along Braids and the Colored Jones Polynomial
• Khovanov homology of a unicolored B-adequate link has a tail
• Jones polynomials, volume, and essential knot surfaces: a survey

Cited by in corpus (6)

• A stability conjecture for the colored Jones polynomial
• Quantum Knot Invariants
• Khovanov homology of a unicolored B-adequate link has a tail
• The Head and Tail of the Colored Jones Polynomial for Adequate Knots
• Flag algebras and the stable coefficients of the Jones polynomial
• The tail of a quantum spin network