Exact Chern-Simons / Topological String duality

Abstract

We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold found elsewhere in the literature, thereby providing strong evidence that the Chern-Simons / topological string duality is exact, and in particular holds at arbitrary N as well. In the refined case, the non-perturbative corrections we find are novel and appear to be non-trivial. We show that non-perturbatively special treatment is needed for rational valued deformation parameter. Above results are also extend to refined Chern-Simons with orthogonal groups.

32 pages

References in corpus (24)

• The Refined Topological Vertex
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Non-perturbative effects and the refined topological string
• Knot Homology from Refined Chern-Simons Theory
• The elliptic gamma function and SL(3,Z) x Z^3
• Extended Holomorphic Anomaly in Gauge Theory
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• Orientifolds, Mirror Symmetry and Superpotentials
• SO and Sp Chern-Simons at Large N
• Universality in Chern-Simons theory
• Nonperturbative universal Chern-Simons theory
• Non-Perturbative Quantum Geometry III
• Orientifolds and the Refined Topological String
• Refined Chern-Simons versus Vogel universality
• Shift versus Extension in Refined Partition Functions
• Refined Chern-Simons Theory and Knot Homology
• The Real Topological Vertex at Work
• The modular properties and the integral representations of the multiple elliptic gamma functions
• Pure N=2 Super Yang-Mills and Exact WKB
• Wall Crossing Phenomenology of Orientifolds
• Holomorphic Anomaly in Gauge Theory on ALE space
• Resummations and Non-Perturbative Corrections
• Volkov's Pentagon for the Modular Quantum Dilogarithm

Cited by in corpus (4)

• Universal volume of groups and anomaly of Vogel's symmetry
• $X_2$ series of universal quantum dimensions
• Exact solutions to quantum spectral curves by topological string theory
• On partition functions of refined Chern-Simons theories on $S^3$