The super Virasoro minimal string arises from quantizing 3d supergravity, with 0A+ and 0B+ dual to the bosonic minimal string matrix integral, 0B- to one with inverse square root singularity, and 0A- having vanishing non-trivial perturbative amplitudes.
Invariants of spectral curves and intersection theory of moduli spaces of complex curves
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abstract
To any spectral curve S, we associate a topological class {\Lambda}(S) in a moduli space M^b_{g,n} of "b-colored" stable Riemann surfaces of given topology (genus g, n boundaries), whose integral coincides with the topological recursion invariants W_{g,n}(S) of the spectral curve S. This formula can be viewed as a generalization of the ELSV formula (whose spectral curve is the Lambert function and the associated class is the Hodge class), or Marino-Vafa formula (whose spectral curve is the mirror curve of the framed vertex, and the associated class is the product of 3 Hodge classes), but for an arbitrary spectral curve. In other words, to a B-model (i.e. a spectral curve) we systematically associate a mirror A-model (integral in a moduli space of "colored" Riemann surfaces). We find that the mirror map, i.e. the relationship between the A-model moduli and B-model moduli, is realized by the Laplace transform.
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Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.
Spectral curve for Eynard-Orantin recursions on dessins d'enfants is related to Narayana numbers.
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The Super Virasoro Minimal String from 3d Supergravity
The super Virasoro minimal string arises from quantizing 3d supergravity, with 0A+ and 0B+ dual to the bosonic minimal string matrix integral, 0B- to one with inverse square root singularity, and 0A- having vanishing non-trivial perturbative amplitudes.
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Les Houches Lectures on Exact WKB Analysis and Painlev\'e Equations
Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.
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Grothendieck's Dessins d'Enfants in a Web of Dualities. II
Spectral curve for Eynard-Orantin recursions on dessins d'enfants is related to Narayana numbers.
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