The paper proves the conifold gap property for Weierstrass elliptic topological recursion and gives an algebraic construction of the rank 5/2 Virasoro Whittaker state, linking the Painlevé I tau function to CFT and holomorphic anomaly approaches.
Refined BPS structures and topological recursion - the Weber and Whittaker curves
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abstract
We study properties of the recently established refined topological recursion for some simple spectral curves associated to quadratic differentials. We prove explicit formulas for the free energy and Voros coefficients of the corresponding quantum curves, and conjecture expressions for all other (smooth) genus zero degree two curves. The results can be written in terms of Bridgeland's notion of refined BPS structure associated to the same initial data, together with a quantum correction to the central charge. The corresponding "invariants" appear to be new, but their interpretation in terms of Donaldson-Thomas theory or QFT is not entirely clear.
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Many-faced Painlev\'e I: irregular conformal blocks, topological recursion, and holomorphic anomaly approaches
The paper proves the conifold gap property for Weierstrass elliptic topological recursion and gives an algebraic construction of the rank 5/2 Virasoro Whittaker state, linking the Painlevé I tau function to CFT and holomorphic anomaly approaches.