Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants
نویسندگان
چکیده
We conjecture that, evaluated at the root of unity exp(2π √ −1/r) instead of the standard exp(π √ −1/r), the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic 3-manifold grow exponentially with growth rates respectively the hyperbolic and the complex volume of the manifold. This reveals a different asymptotic behavior of the relevant quantum invariants than that of Witten’s invariants, that grow polynomially by the Asymptotic Expansion Conjecture. The new phenomenon may indicate a different geometric interpretation of the Reshetikhin-Turaev invariants than the one via the SU(2) Chern-Simons gauge theory. Supporting evidence for the conjectures is provided.
منابع مشابه
Refined invariants and TQFT’s from Homfly skein theory
We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet’s invariants. Roberts’ definition of the Turaev-Viro state sum is exploited. Furthermore, we construct refined Turaev-Viro and Reshetikhin-Turaev TQFT’s and...
متن کاملOn the Absolute Value of the So(3)–invariant and Other Summands of the Turaev–viro Invariant
1. Introduction. It was proved in [S1] and [S2] that each Turaev–Viro invariant T V (M) q for a 3-manifold M is a sum of three invariants T V 0 (M) q , T V 1 (M) q , and T V 2 (M) q (for definition of the Turaev–Viro invariants see [TV]). It follows from the Turaev–Walker theorem (see [T1], [W]) that, up to normalization, T V 0 (M) q coincides with the square of the modulus of the so–called SO(...
متن کاملOn the Spin-refined Reshetikhin-turaev Su(2) Invariants of Lens Spaces
We give an explicit presentation of the value of the spin-refined ReshetikhinTuraev SU(2) invariants of lens spaces. Using this result, we also present the value of spin-refined Turaev-Viro SU(2) invariants of lens spaces.
متن کاملLickorish Invariant and Quantum Osp(1|2)
Since Jones’ seminal work[1], the theories of knots and 3 manifolds have made dramatical progress ( See [2] for a review). By now several approachs are available for constructing the so called quantum invariants of 3 manifolds, notably, the quantum field theoretical approach[3], the quantum group approach[4], Lickorish’s recoupling theory[5], the 6j symbol method of Turaev Viro[6], and the conf...
متن کاملSpin Topological Quantum Field Theories
Starting from the quantum group Uq(sl(2, C)), we construct operator invariants of 3-cobordisms with spin structure, satisfying the requirements of a topological quantum field theory and refining the Reshetikhin–Turaev and Turaev–Viro models. We establish the relationship between these two refined models.
متن کامل