Higher-genus wall-crossing in the gauged linear sigma model

Clader, Emily; Janda, Felix; Ruan, Yongbin

doi:10.1215/00127094-2020-0053

Cited by 9 publications

(8 citation statements)

References 32 publications

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“…(3) During the preparation of this paper, the author learned that Jun Wang independently proved [41] the genus-0 wall-crossing formula for hyper-surfaces in toric stacks for which convexity can fail, and used that to prove a mirror theorem. 1 Motivated by the LG/CY correspondence, there are also similar wall-crossing results on the LG side [16,43]. The method in this paper also works in the setting of K-theoretic Gromov-Witten invariants.…”

Section: Relation To Others' Workmentioning

confidence: 55%

Quasimap wall-crossing for GIT quotients

Zhou

2021

Invent. math.

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In this paper, we prove a wall-crossing formula for -stable quasimaps to GIT quotients conjectured by Ciocan-Fontanine and Kim, for all targets in all genera, including the orbifold case. We prove that stability conditions in adjacent chambers give equivalent invariants, provided that both chambers are stable. In the case of genus-zero quasimaps with one marked point, we compute the invariants in the left-most stable chamber in terms of the small I -function. Using this we prove that the quasimap J -functions are on the Lagrangian cone of the Gromov-Witten theory. The proofs are based on virtual localization on a master space, obtained via some universal construction on the moduli of weighted curves. The fixed-point loci are in one-to-one correspondence with the terms in the wall-crossing formula. Contents

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Section: Relation To Others' Workmentioning

confidence: 55%

Quasimap wall-crossing for GIT quotients

Zhou

2021

Invent. math.

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“…The idea to prove (1.4) is to show that both sides of (1.4) satisfy the same recursive relations (see Theorem 6.3 and Theorem 6.5) by induction on the degree β. This is done by considering two master spaces (see §4.1 and §5.1), which are root stack modification of the twisted graph spaces found in [CJR17a,CJR17b]. Then we apply virtual localization to calculate two auxiliary cycles (see (6.3) and (6.11)) corresponding to two master spaces and extract λ −1 coefficients (λ is an equivariant parameter).…”

Section: Main Results and Ideas Of Proofmentioning

confidence: 99%

“…The main geometrical input in the proof of wall-crossing here is inspired by the twisted graph space used in [CJR17b, CJR17a], where they use the genus zero quasimap wall-crossing as input to prove the high genus quasimap wall-crossing. So it may be surprising that certain modification of the twisted graph space can be used to prove the genus zero quasimap wall-crossing directly.…”

Section: Main Results and Ideas Of Proofmentioning

confidence: 99%

“…Then we will finish the computation of the small I-functions of positive Toric stack hypersurfaces. In §4 and §5, we will construct two master spaces which carry C * -actions, a very explicit C * -localization computation which is based on localization computations [CJR17a,JPPZ17] will be presented, this part is technical, we encourage the reader to skip to go to §6 first and to refer back when needed. In §6, we will calculate two auxiliary cycles corresponding to the two master spaces via localization, they provide recursive relations to prove the genus zero quasimap wall-crossing conjecture for positive toric stack hypersurfaces.…”

Section: Main Results and Ideas Of Proofmentioning

confidence: 99%

“…Construction of master space I. In this section, we will construct a master space which is a root stack modification of the twisted graph space considered in [CJR17a]. Let (AY, G, θ) be the GIT data which gives rise to a hypersurface in the toric stack X = [W ss (θ)/G] as in previous sections.…”

Section: Master Space Imentioning

confidence: 99%

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A mirror theorem for Gromov-Witten theory without convexity

Wang¹

2019

Preprint

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We prove a mirror theorem for all positive hypersurfaces in proper toric Deligne-Mumford stacks, which include all positive hypersurfaces in weighted projective spaces. Here our definition of positivity of a hypersurface depends on the choice of the GIT presentation of the toric stack. Our proof relies on the quasimap theory and consists of two parts: (1) we use the technique of p-fields to compute small I-functions of the positive toric stack hypersurfaces; (2) we prove the genus zero quasimap wall-crossing conjecture for the small I-functions. We expect that the method developed here can be used to provide a mirror theorem for all proper toric Deligne-Mumford stack hypersurfaces.

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On genus-0 invariants of Calabi-Yau hybrid models

Erkinger

Knapp

2023

J. High Energ. Phys.

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We compute genus zero correlators of hybrid phases of Calabi-Yau gauged linear sigma models (GLSMs), i.e. of phases that are Landau-Ginzburg orbifolds fibered over some base. These correlators are generalisations of Gromov-Witten and FJRW invariants. Using previous results on the structure of the of the sphere- and hemisphere partition functions of GLSMs when evaluated in different phases, we extract the I-function and the J-function from a GLSM calculation. The J-function is the generating function of the correlators. We use the field theoretic description of hybrid models to identify the states that are inserted in these correlators. We compute the invariants for examples of one- and two-parameter hybrid models. Our results match with results from mirror symmetry and FJRW theory.

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Higher-genus wall-crossing in the gauged linear sigma model

Cited by 9 publications

References 32 publications

Quasimap wall-crossing for GIT quotients

Quasimap wall-crossing for GIT quotients

A mirror theorem for Gromov-Witten theory without convexity

On genus-0 invariants of Calabi-Yau hybrid models

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