Global Aspects of (0,2) Moduli Space: Toric Varieties and Tangent Bundles

Donagi, Ron; Lu, Zhentao; Melnikov, Ilarion V.

doi:10.1007/s00220-015-2394-9

Cited by 11 publications

(21 citation statements)

References 52 publications

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“…Even for a reductive quotient, one has to provide stability conditions to obtain a well-behaved (though perhaps singular) space. Similar issues arise already in a simpler toric setting [16,27].…”

Section: Redefinitions and Classification Resultsmentioning

confidence: 52%

Small Landau-Ginzburg theories

M.Gholson

Melnikov

2019

J. High Energ. Phys.

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We classify (0,2) Landau-Ginzburg theories that can flow to compact IR fixed points with equal left and right central charges strictly bounded by 3. Our result is a (0,2) generalization of the ADE classification of (2,2) Landau-Ginzburg theories that flow to N=2 minimal models. Unitarity requires the right-moving supersymmetric sector to fall into the standard N=2 minimal model representations, but the left-moving sector need not have supersymmetry. The Landau-Ginzburg realizations provide a simple way to compute the chiral algebra and other characteristics of these fixed points. While our results pertain to isolated superconformal theories, tensor products lead to (0,2) superconformal theories with higher central charge, and the Landau-Ginzburg realization provides a model for a class of marginal and relevant deformations of such theories.

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Section: Redefinitions and Classification Resultsmentioning

confidence: 52%

Small Landau-Ginzburg theories

M.Gholson

Melnikov

2019

J. High Energ. Phys.

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“…For instance, techniques to evaluate B and B/2 model correlators in hybrid models [25,26] have been recently developed [24], and these could be employed to gain insights into this larger set of theories. While we expect a dependence on non-diagonal, but linear, E-parameters, nonlinear E-parameters seem not to affect A/2-twisted V model correlators [27][28][29]. However, the situation is more subtle for A/2-twisted M models, where the supersymmetry constraint relates E and J parameters.…”

Section: Discussionmentioning

confidence: 66%

Testing the (0,2) mirror map

Bertolini

2019

J. High Energ. Phys.

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We test a proposed mirror map at the level of correlators for linear models describing the (0,2) moduli space of superconformal field theories with a (2,2) locus associated to Calabi-Yau hypersurfaces in toric varieties. We verify in non-trivial examples that the correlators are exchanged by the mirror map and we derive a correspondence between the observables of the A/2-and B/2-twisted theories. We also comment on the global structure of the (0,2) moduli space and present a simple non-renormalization argument for a large class of B/2 model subfamilies.

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“…Assume that the deformation on G(k 1 , N 1 ) × G(k 2 , N 2 ) is given by N 1 × N 1 matrices A, B and N 2 × N 2 matrices C, D as in (15). The quantum sheaf cohomology is given by (22). On the other hand, the deformation on G(…”

Section: Note That Quantum Corrections Do Not Change This Results Becamentioning

confidence: 99%

“…Note that deg(q 1 ) = N 1 , deg(q 2 ) = N 2 . We conclude that the quantum sheaf cohomology of 12 , · · · , y 11 , y 12 , · · · , x 21 , x 22 , · · · , y 21 , y 22 , · · · ]/(I + R), (22) where I is the same as the (2,2) case and R is generated by…”

Section: Product Of Grassmanniansmentioning

confidence: 92%

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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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Global Aspects of (0,2) Moduli Space: Toric Varieties and Tangent Bundles

Cited by 11 publications

References 52 publications

Small Landau-Ginzburg theories

Small Landau-Ginzburg theories

Testing the (0,2) mirror map

Quantum Sheaf Cohomology and Duality of Flag Manifolds

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