SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial

Abstract

We clarify and refine the relation between the asymptotic behavior of the colored Jones polynomial and Chern-Simons gauge theory with complex gauge group SL(2,C). The precise comparison requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern-Simons theory. Addressing these issues allows us to go beyond the volume conjecture and to verify some predictions for the behavior of the subleading terms in the asymptotic expansion of the colored Jones polynomial.

arXiv comment15 pages, 7 figures

References in corpus (7)

• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
• Asymptotics of the colored Jones function of a knot
• An analytic version of the Melvin-Morton-Rozansky Conjecture
• Proof of the volume conjecture for Whitehead doubles of a family of torus knots
• Gauge Theoretic Invariants of, Dehn Surgeries on Knots
• A version of the volume conjecture
• The colored Jones polynomials and the Alexander polynomial of the figure-eight knot

Cited by in corpus (31)

• Analytic Continuation Of Chern-Simons Theory
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• A-polynomial, B-model, and Quantization
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• Rotating Black Hole Entropy from M5-branes
• On genus expansion of knot polynomials and hidden structure of Hurwitz tau-functions
• Chern-Simons theory, analytic continuation and arithmetic
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• Colored Kauffman Homology and Super-A-polynomials
• Holography of 3d-3d correspondence at Large N
• On genus expansion of superpolynomials
• A short overview of the "Topological recursion"
• Quantum Riemann Surfaces in Chern-Simons Theory
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• S-duality resurgence in SL(2) Chern-Simons theory
• The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot
• The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory
• Reidemeister torsion, hyperbolic three-manifolds, and character varieties
• Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
• Quantum Knot Invariants
• Schwinger Pair Production in SL$(2,\mathbb{C})$ Topologically Non-Trivial Fields via Non-Abelian Worldline Instantons
• Algebra of quantum $\mathcal{C}$-polynomials
• Rationality of the SL(2,C)-Reidemeister torsion in dimension 3
• On geometric bases for quantum A-polynomials of knots
• Asymptotics of some quantum invariants of the Whitehead chains
• On knots, complements, and 6j-symbols
• Quantum Field Theory and the Volume Conjecture
• Volume conjecture, geometric decomposition and deformation of hyperbolic structures
• On geometric bases for A-polynomials II: ${\mathfrak{su}}_3$ and Kuberberg bracket
• The Kauffman skein module at first order