Invariants of spectral curves and intersection theory of moduli spaces of complex curves

Abstract

To any spectral curve S, we associate a topological class Λ(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.

Latex, 38 pages, 6 figures

References in corpus (9)

• Open string amplitudes and large order behavior in topological string theory
• Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
• Symplectic invariants, Virasoro constraints and Givental decomposition
• Intersection numbers of spectral curves
• Local Mirror Symmetry for One-Legged Topological Vertex
• CFT and topological recursion
• Invariants of algebraic curves and topological expansion
• Bouchard-Klemm-Marino-Pasquetti Conjecture for ${\mathbb{C}}^3$
• Evaluating tautological classes using only Hurwitz numbers

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• A Unified Approach to Holomorphic Anomaly Equations and Quantum Spectral Curves
• Large genus behavior of topological recursion
• A formalism of abstract quantum field theory of summation of fat graphs
• Les Houches lecture notes on moduli spaces of Riemann surfaces
• Combinatorics of KP hierarchy structural constants