The Eynard–Orantin recursion and equivariant mirror symmetry for the projective line

Fang, Bohan; Liu, Chiu-Chu Melissa; Zong, Zhengyu

doi:10.2140/gt.2017.21.2049

Cited by 23 publications

(26 citation statements)

References 35 publications

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“…Application of topological recursion (TR) to constructing generating functions for cohomological field theories is becoming an important issue in contemporary mathematical physics (see, e.g., the recent paper [23] where all genus all descendants equivariant Gromov-Witten invariants of P 1 were constructed using TR). In this respect, it seems interesting to understand the status of Givental-type decompositions in the quantum spectral curve approach.…”

Section: Resultsmentioning

confidence: 99%

Topological recursion for Gaussian means and cohomological field theories

et al. 2015

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We use the explicit relation between genus filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M disc g,s (discrete volumes), to express Gaussian means in all genera as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate topological recursion of the Gaussian model into recurrent relations for coefficients of this expansion proving their integrality and positivity. As an application, we find the coefficients in the first subleading order for M g,1 for all g in three ways: by using the refined Harer-Zagier recursion, by exploiting the Givental-type decomposition of KPMM, and by an explicit diagram counting.

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Section: Resultsmentioning

confidence: 99%

Topological recursion for Gaussian means and cohomological field theories

et al. 2015

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“…Although topological recursion was originally inspired by the loop equations in the theory of matrix models, it has over the last decade found widespread applications to various problems across mathematics and physics. For example, it is known to govern the enumeration of maps on surfaces [3,18,19,21,22,31,35], various flavours of Hurwitz problems [9,11,16,17,24], the Gromov-Witten theory of P 1 [23,36] and toric Calabi-Yau threefolds [10,25,28]. There are also conjectural relations to quantum invariants of knots [6,15].…”

Section: Introductionmentioning

confidence: 99%

Topological recursion on the Bessel curve

Norbury

2018

Communications in Number Theory and Physics

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The Witten-Kontsevich theorem states that a certain generating function for intersection numbers on the moduli space of stable curves is a tau-function for the KdV integrable hierarchy. This generating function can be recovered via the topological recursion applied to the Airy curve x = 1 2 y 2 . In this paper, we consider the topological recursion applied to the irregular spectral curve xy 2 = 1 2 , which we call the Bessel curve. We prove that the associated partition function is also a KdV tau-function, which satisfies Virasoro constraints, a cut-and-join type recursion, and a quantum curve equation. Together, the Airy and Bessel curves govern the local behaviour of all spectral curves with simple branch points.

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“…In the simplest case one can say that the Frobenius manifold with the prepotential t 2 1 t 2 /2 + t 2 2 log t 2 resolves, via its associated CohFT and the ELSV-type formula, the combinatorial problem known, in different versions, as generalized Catalan numbers, discrete volumes of moduli spaces, or discrete surfaces [1,9,17,27]. This explains, in a conceptual way, some observations already made in [2,19].…”

Section: Enumeration Of Hypermapsmentioning

confidence: 78%