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

By B. Eynard. 2011

139 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e847a59bb43f8cd002c8251357ca62e80b70c1e5

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture (2012, background): “2 (corrolary of the theorem in [16, 3, 53, 38]) Let S = (C, x, y, B) be a spectral curve with branchpoints {a1, .”
Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, background): “1 2 exp − X∞ j=1 Bj+1( 1 r ) j(j+ 1) w−j ! , which proves (28) X∞ j=0 Vjw −j = exp − X∞ j=1 Bj+1( 1 r ) j(j+ 1) w−j ! . ⋄ 4.3. Two-point function. Now we consider the two-point function. According to [16], since dxis a meromorphic 1-form in y, we know that the Laplace transform of the two-point func”
Identification of the Givental Formula with the Spectral Curve Topological Recursion Procedure (2012, methodology): “n expansion near a simple critical point of the spectral curve, see [11]). Moreover, in both cases we have an expansion of the correlators in terms of Feynman graphs, see [8] on the Givental side and [12, 16, 21] on the spectral curve side. So, the natural question is whether we can precisely identi”
Weighted Hurwitz Numbers and Topological Recursion (2018, methodology): “There has also been important progress in relating Hurwitz numbers to other classes of enumerative geometric invariants [2, 21,26,33,40,55,65,68,69,72] and matrix models [1, 6–9,17,21,25,61,64,68,69].”