GLSMs for exotic Grassmannians

Gu, Wei; Sharpe, Eric; Zou, Hao

doi:10.1007/jhep10(2020)200

Cited by 6 publications

(5 citation statements)

References 40 publications

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“…In this section, we focus on two special cases: symplectic Grassmannian and complete symplectic flag manifold. The quantum cohomology rings of both cases have already been found and proved in the literature [22,[24][25][26]. We will show that our result reproduces the existing results when specialized to these two cases.…”

Section: Reduction To Previous Resultssupporting

confidence: 84%

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Quantum cohomology of symplectic flag manifolds

Guo¹,

Zou²

2022

J. Phys. A: Math. Theor.

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We compute the quantum cohomology of symplectic flag manifolds. The ring structure was known in the special cases of symplectic Grassmannians and complete symplectic flag manifolds. Starting from a GLSM construction, our computation gives the ring structure of quantum cohomology for all symplectic flag manifolds. Symplectic flag manifolds can be described by non-abelian GLSMs with superpotential. Although the ring relations cannot be directly read off from the equations of motion on the Coulomb branch due to the complication introduced by the non-abelian gauge symmetry, it can be shown that they can be extracted from the localization formula in a gauge-invariant form. We show that, when restricted to symplectic Grassmannians and complete symplectic flag manifolds, our general result reduces to the previously established results derived by other means. We also explain why a (0,2) deformation of the GLSM does not give rise to a deformation of the quantum cohomology.

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Section: Reduction To Previous Resultssupporting

confidence: 84%

“…[5-7, 11, 12, 19-21, 23]). In this work, we derive the ring structure for symplectic flag manifolds, which can be described by non-abelian GLSMs [22]. This problem has been studied before in two special cases, namely the symplectic Grassmannians [24,25] and the complete symplectic flag manifolds [26].…”

Section: Introductionmentioning

confidence: 99%

Quantum cohomology of symplectic flag manifolds

Guo¹,

Zou²

2022

J. Phys. A: Math. Theor.

Self Cite

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show abstract

“…In this section, we focus on two special cases: symplectic Grassmannian and complete symplectic flag manifold. The quantum cohomology rings of both cases have already been found and proved in the literature [21,[23][24][25]. We will show that our result reproduces the existing results when specialized to these two cases.…”

Section: Reduction To Previous Resultssupporting

confidence: 84%

“…As reasoned in [21,Section 2.6], the geometric phase of this gauge theory realizes the symplectic flag manifold SF (k 1 , k 2 , . .…”

Section: Now We Give a Description Of The Classical Cohomology Ring Of Sfmentioning

confidence: 93%

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Quantum Sheaf Cohomology and Duality of Flag Manifolds

Guo

2019

Commun. Math. Phys.

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We study the quantum sheaf cohomology of flag manifolds with deformations of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds. Realized as the OPE ring of A/2-twisted twodimensional theories with (0,2) supersymmetry, quantum sheaf cohomology generalizes the notion of quantum cohomology. Complete descriptions of quantum sheaf cohomology have been obtained for abelian gauged linear sigma models (GLSMs) and for nonabelian GLSMs describing Grassmannians. In this paper we continue to explore the quantum sheaf cohomology of nonabelian theories. We first propose a method to compute the generating relations for (0,2) GLSMs with (2,2) locus. We apply this method to derive the quantum sheaf cohomology of products of Grassmannians and flag manifolds. The dual deformation associated with the biholomorphic duality gives rise to an explicit IR duality of two A/2-twisted (0,2) gauge theories.

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Non-Abelian T-dualities in two dimensional (0, 2) gauged linear sigma models

Bizet,

Díaz-Correa,

García-Compeán

2024

J. High Energ. Phys.

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We consider two dimensional (2D) gauged linear sigma models (GLSMs) with (0, 2) supersymmetry and U(1) gauge group which posses global symmetries. We distinguish between two cases: one obtained as a reduction from the (2, 2) supersymmetric GLSM and another not coming from a reduction. In the first case we find the Abelian T-dual, comparing with previous studies. Then, the Abelian T-dual model of the second case is found. Instanton corrections are also discussed in both situations. We explore the vacua for the scalar potential and we analyse the target space geometry of the dual model. An example with gauge symmetry U(1) × U(1) is discussed, which posses non-Abelian global symmetry. Non-Abelian T-dualization of U(1) (0, 2) 2D GLSMs is implemented for models that arise as a reduction from the (2, 2) case; we study a model with U(1) gauge symmetry and SU(2) global symmetry. It is shown that for a positive definite scalar potential, the dual vacua to $${\mathbb{P}}^{1}$$ constitutes a disk. Instanton corrections to the superpotential are obtained and are shown to be encoded in a shift of the holomorphic function E. We conclude by analyzing an example with SU(2) × SU(2) global symmetry, obtaining that the space of dual vacua to $${\mathbb{P}}^{1}$$ × $${\mathbb{P}}^{1}$$ consists of two copies of the disk, also for the case of positive definite potential. Here we are able to fully integrate the equations of motion of non-Abelian T-duality, improving the analysis with respect to the studies in (2, 2) models.

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GLSMs for exotic Grassmannians

Cited by 6 publications

References 40 publications

Quantum cohomology of symplectic flag manifolds

Quantum cohomology of symplectic flag manifolds

Quantum Sheaf Cohomology and Duality of Flag Manifolds

Non-Abelian T-dualities in two dimensional (0, 2) gauged linear sigma models

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