(0,2) Mirror Symmetry on Homogeneous Hopf Surfaces

Álvarez-Cónsul, Luis; Hera, Andoni De Arriba de La; Garcia-Fernandez, Mario

doi:10.1093/imrn/rnad016

Cited by 2 publications

(2 citation statements)

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“…The Hull-Strominger system has recently generated a great deal of interest in mathematics, both for its applications to the study of non-Kähler Calabi-Yau manifolds [16,26,47] and its relation to a conjectural generalization of mirror symmetry [1,51]. As originally proposed in the seminal work by Li-Yau [42] and Fu-Yau [22,23] on these equations, it is expected that the Hull-Strominger system plays a key role on the geometrization of Reid's fantasy [11,20], connecting complex threefolds with trivial canonical bundle via conifold transitions.…”

Section: Introductionmentioning

confidence: 99%

“…As for the geometry, solutions of (1.1) satisfying (1.4) are generalized Ricci flat [25,27] and have a moment map interpretation [7,35], which leads to an interesting metric on its moduli space. Furthermore, there is currently strong evidence that these solutions play an important role in (0,2) mirror symmetry via T-duality and the theory of vertex algebras [1,6,28].…”

Section: Introductionmentioning

confidence: 99%

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Futaki Invariants and Yau's Conjecture on the Hull-Strominger system

Garcia-Fernandez¹,

Molina²

2023

Preprint

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We find a new obstruction to the existence of solutions of the Hull-Strominger system, which goes beyond the balanced property of the Calabi-Yau manifold (X, Ω) and the Mumford-Takemoto slope stability of the bundle over it. The basic principle is the construction of a (possibly indefinite) Hermitian-Einstein metric on the holomorphic string algebroid associated to a solution of the system, provided that the connection ∇ on the tangent bundle is Hermitian-Yang-Mills. Using this, we define a family of Futaki invariants obstructing the existence of solutions in a given balanced class. Our results are motivated by a strong version of a conjecture by Yau on the existence problem for these equations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Futaki Invariants and Yau's Conjecture on the Hull-Strominger system

Garcia-Fernandez¹,

Molina²

2023

Preprint

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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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(0,2) Mirror Symmetry on Homogeneous Hopf Surfaces

Cited by 2 publications

References 50 publications

Futaki Invariants and Yau's Conjecture on the Hull-Strominger system

Futaki Invariants and Yau's Conjecture on the Hull-Strominger system

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

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