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Mirror of the refined topological vertex from a matrix model
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We find an explicit matrix model computing the refined topological vertex, starting from its representation in terms of plane partitions. We then find the spectral curve of that matrix model, and thus the mirror symmetry of the refined vertex. With the same method we also find a matrix model for the strip geometry, and we find its mirror curve. The fact that there is a matrix model shows that the refined topological string amplitudes also satisfy the remodeling the B-model construction.
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Geometry of Logarithmic Topological Recursion: Dilaton Equations, Free Energies and Variational Formulas
Logarithmic topological recursion supplies dilaton equations and free-energy definitions that match the Nekrasov-Shatashvili perturbative partition function and all-genus mirror-curve free energies directly.
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