Open $r$-spin theory II: The analogue of Witten's conjecture for $r$-spin disks

Buryak, Alexandr; Clader, Emily; Tessler, Ran J.

doi:10.48550/arxiv.1809.02536

Cited by 7 publications

(37 citation statements)

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“…This fact, and transversality arguments, show that if such multisections can be found, the intersection numbers that they define will be independent of the choice of the specific coherent multisections. A similar idea has already appeared in [3,4,31] and related papers in their definitions of open intersection numbers. In those papers, and here as well, the scheme of boundary conditions gives rise to a beautiful enumerative theory.…”

Section: 3mentioning

confidence: 70%

“…(a) First, in the introduction another definition for open intersection numbers was sketched, as the weighted cardinality of the intersection of the zero loci of multisections of L i , given some boundary conditions. That approach, which is similar to the approach taken in [31,3,4], can be made fully rigourous by a recursive construction analogous to those given in these papers.…”

Section: 5mentioning

confidence: 96%

“…By analogy to the closed GW theory of CP 1 , we have divisor equations and topological recursions (compare to the TRRs of [31,3,4]) also in the open setting.…”

Section: 3mentioning

confidence: 99%

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Open $\mathbb{CP}^1$ descendent theory I: The stationary sector

Buryak,

Zernik,

Pandharipande

et al. 2020

Preprint

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We define stationary descendent integrals on the moduli space of stable maps from disks to (CP 1 , RP 1 ). We prove a localization formula for the stationary theory involving contributions from the fixed points and from all the corner-strata. We use the localization formula to prove a recursion relation and a closed formula for all genus 0 disk cover invariants in the stationary case. For all higher genus invariants, we propose a conjectural formula.

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Section: 3mentioning

confidence: 70%

Section: 5mentioning

confidence: 96%

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Open $\mathbb{CP}^1$ descendent theory I: The stationary sector

Buryak,

Zernik,

Pandharipande

et al. 2020

Preprint

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“…where 1 ≤ α, β, γ ≤ N + 1. These equations appear in open Gromov-Witten theory [HS12, ST19,CZ21], open r-spin theory [BCT18] (see [Bur20,Section 4] explaining that the open topological recursion relations in genus 0 appearing in [BCT18] imply the open WDVV equations), and also in [BB21] in the context of open Saito theory. The system of equations (1.1) and (1.4) is equivalent to the fact that the tensor…”

Section: 3mentioning

confidence: 99%

A construction of open descendant potentials in all genera

Alexandrov¹,

Basalaev²,

Buryak³

2022

Preprint

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We present a construction of an open analogue of total descendant and total ancestor potentials via an "open version" of Givental's action. Our construction gives a genus expansion for an arbitrary solution to the open WDVV equations satisfying a semisimplicity condition and admitting a unit. We show that the open total descendant potentials we define satisfy the open topological recursion relations in genus 0 and 1, the open string and open dilaton equations. Contents 1. Introduction 1 2. A Givental-type theory for solutions to the open WDVV equations 6 3. Open total descendant potentials 17 4. Proof of Theorem 2 22 References 27 *Applying to the pair, ε) a certain shift, a linear change of variables, and the G o N +1,+ -action, we obtain a space of pairs (F c,anc , F o,anc ), where F c,anc is a closed total ancestor potential, and F o,anc is a new function, which we call an open total ancestor potential.

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“…Buryak, Clader, and Tessler recently constructed an open r-spin enumerative theory [BCT21,BCT18], following the case of descendent invariants on the moduli space of holomorphic disks developed by Pandharipande, Solomon and Tessler in [PST14]. Roughly stated, they construct a moduli space of r-stable orbidisks with r-spin structures that have prescribed twists at both internal and boundary marked points.…”

Section: Introductionmentioning

confidence: 99%

Mirror Symmetry for open r-spin invariants

Gross¹,

Kelly²,

Tessler³

2022

Preprint

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We show that a generating function for open r-spin enumerative invariants produces a universal unfolding of the polynomial x r . Further, the coordinates parametrizing this universal unfolding are flat coordinates on the Frobenius manifold associated to the Landau-Ginzburg model (C, x r ) via Saito-Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel [GKT22].

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Open $r$-spin theory II: The analogue of Witten's conjecture for $r$-spin disks

Cited by 7 publications

References 0 publications

Open $\mathbb{CP}^1$ descendent theory I: The stationary sector

Open $\mathbb{CP}^1$ descendent theory I: The stationary sector

A construction of open descendant potentials in all genera

Mirror Symmetry for open r-spin invariants

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