BHK mirror symmetry for K3 surfaces with non-symplectic automorphism

Comparin, Paola; Priddis, Nathan

doi:10.2969/jmsj/79867986

Cited by 9 publications

(27 citation statements)

References 28 publications

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“…in a weighted projective space, and supersymmetric quotients thereof. As was shown in [14], using recent mathematical results [27][28][29][30], the diagonal action of an order p purely nonsymplectic automorphim σ p acting on a surface of type (2.3) and of the corresponding order p automorphismσ p of the mirror surface (in the Greene-Plesser [31]/Berglund-Hübsch [32] sense) can be lifted to a mirrored automorphism σ p of non-linear sigma models on K3, corresponding to a certain element of the orthogonal group O(Γ 4,20 ). Importantly, the action of σ p leaves no sub-lattice of Γ 4,20 invariant, and its matrix representation M p can JHEP09(2020)082…”

Section: Brief Presentation Of the Modelsmentioning

confidence: 81%

Moduli spaces of non-geometric type II/heterotic dual pairs

Gautier

Israël

2020

J. High Energ. Phys.

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We study the moduli spaces of heterotic/type II dual pairs in four dimensions with $$ \mathcal{N} $$ N = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non- perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α′.

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Section: Brief Presentation Of the Modelsmentioning

confidence: 81%

Moduli spaces of non-geometric type II/heterotic dual pairs

Gautier

Israël

2020

J. High Energ. Phys.

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“…This result has been proved for n = 2 by Artebani, Boissière and Sarti in [1] and for n prime by Comparin, Lyons, Priddis and Suggs in [15], and for all other n, except for n = 4, 8, 12 in [16]. In all cases, the proof of the theorem is done computing the invariant lattices S(σ n ) and S(σ T n ) for the K3 surfaces X W,G and X W T ,G T and then comparing them, in order to show they are mirror lattices.…”

Section: Introductionmentioning

confidence: 68%

“…Such relations are no longer avalaible when n is not prime, so that in [16] the authors introduce new methods for computing S(σ n ) in order to prove the theorem for n composite and different from 4, 8, 12. However, these methods we not sufficient for n = 4, 8, 12.…”

Section: Introductionmentioning

confidence: 99%

Mirror symmetry for K3 surfaces

Bott

Comparin

Priddis

2019

Preprint

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For certain K3 surfaces, there are two constructions of mirror symmetry that are very different. The first, known as BHK mirror symmetry, comes from the Landau-Ginzburg model for the K3 surface; the other, known as LPK3 mirror symmetry, is based on a lattice polarization of the K3 surface in the sense of Dolgachev's definition. There is a large class of K3 surfaces for which both versions of mirror symmetry apply. In this class we consider the K3 surfaces admitting a certain purely nonsymplectic automorphism of order 4, 8, or 12, and we complete the proof that these two formulations of mirror symmetry agree for this class of K3 surfaces.

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“…in a weighted projective space, and supersymmetric quotients thereof. As was shown in [14], using recent mathematical results [24][25][26][27], the diagonal action of an order p purely non-symplectic automorphim σ p acting on a surface of type (2.3) and of the corresponding order p automorphism σp of the mirror surface (in the Greene-Plesser [28]/Berglund-Hübsch [29] sense) can be lifted to a mirrored automorphism σ p of non-linear sigma models on K3, corresponding to a certain element of the orthogonal group O(Γ 4,20 ). Importantly, the action of σ p leaves no sub-lattice of Γ 4,20 invariant, and its matrix representation M p can be diagonalized over C as 1…”

Section: Brief Presentation Of the Modelsmentioning

confidence: 81%

Moduli spaces of non-geometric type II/heterotic dual pairs

Gautier,

Israel

2020

Preprint

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We study the moduli spaces of heterotic/type II dual pairs in four dimensions with N = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non-perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α ′ .

show abstract

BHK mirror symmetry for K3 surfaces with non-symplectic automorphism

Cited by 9 publications

References 28 publications

Moduli spaces of non-geometric type II/heterotic dual pairs

Moduli spaces of non-geometric type II/heterotic dual pairs

Mirror symmetry for K3 surfaces

Moduli spaces of non-geometric type II/heterotic dual pairs

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