On a Gopakumar-Vafa form of partition function of Chern-Simons theory on classical and exceptional lines
arXiv:1410.0376 · doi:10.1007/JHEP12(2014)171
Abstract
We show that partition function of Chern-Simons theory on three-sphere with classical and exceptional groups (actually on the whole corresponding lines in Vogel's plane) can be represented as ratio of respectively triple and double sine functions (last function is essentially a modular quantum dilogarithm). The product representation of sine functions gives Gopakumar-Vafa structure form of partition function, which in turn gives a corresponding integer invariants of manifold after geometrical transition. In this way we suggest to extend gauge/string duality to exceptional groups, although one still have to resolve few problems. In both classical and exceptional cases an additional terms, non-perturbative w.r.t. the string coupling constant, appear. The full universal partition function of Chern-Simons theory on three-sphere is shown to be the ratio of quadruple sine functions. We also briefly discuss the matrix model for exceptional line.
arXiv comment22 pages, all formulae remain the same, text reflects their content better
References in corpus (14)
- Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
- Discrete Heisenberg-Weyl Group and Modular Group
- Worldsheet Derivation of a Large N Duality
- Chern-Simons Theory and Topological Strings
- Virasoro constraints and the Chern classes of the Hodge bundle
- Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
- Noncommutative Hypergeometry
- Topological Open String Amplitudes On Orientifolds
- Universality in Chern-Simons theory
- Nonperturbative universal Chern-Simons theory
- Casimir eigenvalues for universal Lie algebra
- Counting Higher Genus Curves with Crosscaps in Calabi-Yau Orientifolds
- Universal Chern-Simons partition functions as quadruple Barnes' gamma-functions
- Caracteres sur l'algebre de diagrammes trivalents Lambda