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

2011/10/13 by Eynard, B. · 2 citations
#14Nxx #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1110.2949

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.

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