D-brane central charge and Landau-Ginzburg orbifolds

Knapp, Johanna; Romo, Mauricio; Scheidegger, Emanuel

doi:10.48550/arxiv.2003.00182

Cited by 4 publications

(34 citation statements)

References 89 publications

(287 reference statements)

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“…This suggests that the relation (3.3) is a realisation of the matrix M (2.10) that implements CPT conjugation. Similar observations have been made in [16] in the context of the D-brane central charge, where spectral flow was required to relate the pairing between the (a, c)-and (c, c)-rings to the topological pairing.…”

Section: Tt * -Geometrysupporting

confidence: 56%

“…This provides a framework to define and compute the objects entering (1.1). First we give more details on Landau-Ginzburg models where explicit expressions for the ingredients of (1.1) have been given recently [16]. Then we comment on geometric and hybrid phases.…”

Section: Sphere Partition Function and Tt *mentioning

confidence: 99%

“…In our discussion we mostly follow [35][36][37][38]. For a review in the spirit of this paper see [16]. We consider an N = (2, 2) theory in two dimensions with a mass gap.…”

Section: Tt * -Geometrymentioning

confidence: 99%

“…The two choices of coordinates are related by a coordinate change. In geometric phases and Landau-Ginzburg phases it is known how to extract this information from the results of supersymmetric localisation [5,16]. It coincides with the mirror map and exchanges I-and J-functions.…”

Section: Tt * -Geometrymentioning

confidence: 99%

“…In [16] it was proposed that the hemisphere partition function of a Calabi-Yau GLSM, which conjecturally computes the exact central charge of a D-brane, has the same structure in every phase. This was shown to hold for geometric and Landau-Ginzburg phases.…”

Section: Introductionmentioning

confidence: 99%

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Sphere partition function of Calabi-Yau GLSMs

Erkinger¹,

Knapp²

2020

Preprint

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The sphere partition function of Calabi-Yau gauged linear sigma models (GLSMs) has been shown to compute the exact Kähler potential of the Kähler moduli space of a Calabi-Yau. We propose a universal expression for the sphere partition function evaluated in hybrid phases of Calabi-Yau GLSMs that are fibrations of Landau-Ginzburg orbifolds over some base manifold. Special cases include Calabi-Yau complete intersections in toric ambient spaces and Landau-Ginzburg orbifolds. The key ingredients that enter the expression are Givental's I/J-functions, the Gamma class and further data associated to the hybrid model. We test the proposal for one-and two-parameter abelian GLSMs, making connections, where possible, to known results from mirror symmetry and FJRW theory.

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Section: Tt * -Geometrysupporting

confidence: 56%

Section: Sphere Partition Function and Tt *mentioning

confidence: 99%

“…In our discussion we mostly follow [35][36][37][38]. For a review in the spirit of this paper see [16]. We consider an N = (2, 2) theory in two dimensions with a mass gap.…”

Section: Tt * -Geometrymentioning

confidence: 99%

Section: Tt * -Geometrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sphere partition function of Calabi-Yau GLSMs

Erkinger¹,

Knapp²

2020

Preprint

Self Cite

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Sphere Partition Function of Calabi–Yau GLSMs

Erkinger

Knapp

2022

Commun. Math. Phys.

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The sphere partition function of Calabi–Yau gauged linear sigma models (GLSMs) has been shown to compute the exact Kähler potential of the Kähler moduli space of a Calabi–Yau. We propose a universal expression for the sphere partition function evaluated in hybrid phases of Calabi–Yau GLSMs that are fibrations of Landau–Ginzburg orbifolds over some base manifold. Special cases include Calabi–Yau complete intersections in toric ambient spaces and Landau–Ginzburg orbifolds. The key ingredients that enter the expression are Givental’s I/J-functions, the Gamma class and further data associated to the hybrid model. We test the proposal for one- and two-parameter abelian GLSMs, making connections, where possible, to known results from mirror symmetry and FJRW theory.

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Liouville conformal blocks and Stokes phenomena

Gu,

Haghighat

2024

Beijing Journal of Pure and Applied Mathematics

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Dedicated to Professor Sergio Cecotti on the occasion of joining BIMSA as a faculty memberWe explore how B-branes in two-dimensional N = (2, 2) anomalous models behave as we vary the energy scale and bulk parameters in the quantum Kähler moduli space. We focus on (2, 2) theories defined by abelian gauged linear sigma models (GLSM). Guided by the hemisphere partition function we find how B-branes split in arbirary phases into components on the Higgs branch and other branches: this generalizes the band restriction rules of Herbst-Hori-Page to (abelian) anomalous models.Secondly, we address divergences in non-compact models, through the central example of GLSMs for Hirzebruch-Jung resolutions of cyclic surface singularities. For a brane with compact support we explain how to regularize and compute the hemisphere partition function and extract its Higgs branch component, which we match in the zero-instanton sector to the geometric central charge of the brane. To this aim, we clarify the definition of zeroinstanton geometric central charge for objects in the derived category of a non-compact toric orbifold.

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D-brane central charge and Landau-Ginzburg orbifolds

Cited by 4 publications

References 89 publications

Sphere partition function of Calabi-Yau GLSMs

Sphere partition function of Calabi-Yau GLSMs

Sphere Partition Function of Calabi–Yau GLSMs

Liouville conformal blocks and Stokes phenomena

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