Deformed quantum cohomology and (0,2) mirror symmetry

Guffin, Josh; Katz, Sheldon

doi:10.1007/jhep08(2010)109

Cited by 28 publications

(74 citation statements)

References 27 publications

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“…There are two sets of techniques available to compute correlators in the A/2-twisted V-model: the approach of [11], which uses algebraic techniques to compute sheaf cohomology on the instanton moduli space; and an approach that computes the entire instanton series by extending (2,2) Coulomb branch techniques [14] to include linear E-parameters [13]. The first method is powerful-for instance, it should be able to determine any dependence on the non-linear E-deformations-but requires a bit of commutative algebra machinery and work at the level ofČech co-chains.…”

Section: A Summary Of the Resultsmentioning

confidence: 99%

“…The second method, though currently restricted to linear deformations, is computationally simpler to use and provides a quick route to quantum cohomology. In section 3.5 we propose a third method that avoids some of the complications of [11] and closely resembles the familiar toric intersection theory on instanton moduli space available on the (2,2) locus.…”

Section: A Summary Of the Resultsmentioning

confidence: 99%

“…In the case when V is a toric variety, the GLSM naturally provides such a compactification. The ideas in [10] were refined and developed in [11], culminating in a general method for computing the A/2 correlators in the V-model. The result should be thought of as a quantum deformation of the intersection ring on…”

Section: The A/2-twisted V-model In the Geometric Phasementioning

confidence: 99%

“…While the method of [10,11] is well-motivated and leads to sensible results, a number of questions naturally arise. First, can we be sure that the linear model pathintegral is compputed by this sheaf cohomology on the instanton moduli space?…”

Section: The A/2-twisted V-model In the Geometric Phasementioning

confidence: 99%

“…We refer to these as the A/2 and B/2 twists. Finally, studies of halftwisted massive (0,2) linear sigma models and Landau-Ginzburg theories have shown that these rings are eminently computable and provide a non-trivial generalization of quantum cohomology [8,10,11]. These findings suggest that there may be a well-defined mirror map, exchanging A/2-twisted and B/2-twisted theories.…”

Section: Introductionmentioning

confidence: 98%

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Summing the instantons in half-twisted linear sigma models

McOrist

Melnikov

2009

J. High Energy Phys.

122

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We study half-twisted linear sigma models relevant to (0,2) compactifications of the heterotic string. Focusing on theories with a (2,2) locus, we examine the linear model parameter space and the dependence of genus zero half-twisted correlators on these parameters. We show that in a class of theories the correlators and parameters separate into A and B types, present techniques to compute the dependence, and apply these to some examples. These results should bear on the mathematics of (0,2) mirror symmetry and the physics of the moduli space and Yukawa couplings in heterotic compactifications.

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Section: A Summary Of the Resultsmentioning

confidence: 99%

Section: A Summary Of the Resultsmentioning

confidence: 99%

Section: The A/2-twisted V-model In the Geometric Phasementioning

confidence: 99%

Section: The A/2-twisted V-model In the Geometric Phasementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Summing the instantons in half-twisted linear sigma models

McOrist

Melnikov

2009

J. High Energy Phys.

122

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Target spaces from chiral gauge theories

Melnikov

Quigley

Sethi

et al. 2013

J. High Energ. Phys.

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Chiral gauge theories in two dimensions with (0, 2) supersymmetry are central in the study of string compactifications. Remarkably little is known about generic (0, 2) theories. We consider theories with branches on which multiplets with a net gauge anomaly become massive. The simplest example is a relevant perturbation of the gauge theory that flows to the CP n model. To compute the effective action, we derive a useful set of Feynman rules for (0, 2) supergraphs. From the effective action, we see that the infra-red geometry reflects the gauge anomaly by the presence of a boundary at finite distance. In generic examples, there are boundaries, fluxes and branes; the resulting spaces are non-Kähler.

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Localization of twisted N = 0 , 2 $$ \mathcal{N}=\left(0,\;2\right) $$ gauged linear sigma models in two dimensions

Closset

Jia

et al. 2016

J. High Energ. Phys.

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We study two-dimensional N =(0, 2) supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider N =(0, 2) theories with an R-symmetry, which can always be defined on curved space by a pseudotopological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of N =(2, 2) GLSMs and retain a Coulomb branch, we consider the A/2-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the N =(2, 2) locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the N =(2, 2) locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the Grassmannian manifold. Keywords: Supersymmetry, Topological Field Theory. A. Conventions and review of N =(0, 2) supersymmetry 40 A.1 Curved space conventions 40 A.2 N =(0, 2) supersymmetry in flat space 40 B. Elementary properties of the Grothendieck residue 43 C. One-loop determinants 44 C.1 Matter determinant for A/2-twisted GLSM with (2, 2) locus 44 C.2 Matter determinant for the B/2-twisted model 46 D.Čech-cohomology-based results for the correlation functions 46 D.1 P 1 × P 1 46 D.2Čech-cohomology-based results for F 1 49 R[E I ] = r I + 1 , R[J I ] = 1 − r I , (2.49) and such that Tr( Λ I E I ) and Tr(Λ I J I ) are gauge invariant.Anomaly cancelation imposes further constraints on the matter content and on the R-charge assignment. Let us decompose the gauge algebra g into semi-simple factors g α

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Deformed quantum cohomology and (0,2) mirror symmetry

Cited by 28 publications

References 27 publications

Summing the instantons in half-twisted linear sigma models

Summing the instantons in half-twisted linear sigma models

Target spaces from chiral gauge theories

Localization of twisted N = 0 , 2 $$ \mathcal{N}=\left(0,\;2\right) $$ gauged linear sigma models in two dimensions

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