Topological strings and Wilson loops

Abstract

We propose the refined topological string correspondence to the expectation values of half-BPS Wilson loop operators in 5d $\mathcal{N}=1$ gauge theory partition function on the Omega-deformed background ${\mathbb{R}}_{{\epsilon }_{1,2}}^4\times S^1$. We provide the refined topological vertex method and the refined holomorphic anomaly equation method in the topological string theory, from which we have exact computations on the 5d Wilson loops partition functions in both A- and B-models. Finally, with the exact results we have in B-model, we recover the quantum periods of local ${\mathbb{P}}^1\times {\mathbb{P}}^1$ model and local ${\mathbb{P}}^2$ model in the study of quantum geometry and we further give a refined generalization of A-period.

61 pages, 11 figures

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Cited by in corpus (5)

• On the resurgent structure of quantum periods
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• On a 5D UV completion of Argyres-Douglas theories
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations