(0,2) Duality

Adams, Allan; Basu, Anirban; Sethi, Savdeep

doi:10.4310/atmp.2003.v7.n5.a5

Cited by 81 publications

(198 citation statements)

References 38 publications

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“…Such bundles are studied in [18,19] if X is a toric variety. We do not develop these techniques here since one of our goals in the present paper is to verify the claims of [1] and the gauge bundles appearing there are not of this type. It would nevertheless be interesting to develop computational techniques for this equivariant situation.…”

Section: Stable Maps and Compactificationsmentioning

confidence: 99%

“…In section 6 we review how linear sigma models can be used to provide a natural compactification, and furthermore how they naturally define and extend the relevant sheaves, in a fashion compatible with symmetries. Finally in section 7 we apply this technology to check some predictions of [1].…”

Section: Ch 2 (E) = Ch 2 (T X)mentioning

confidence: 99%

“…Technically, although we will sometimes speak of heterotic chiral 'rings,' following [1], in general one will not always have a well-behaved ring structure. It would be more accurate to say that we will study correlation functions between certain operators in (0, 2) models, which in certain special cases (e.g.…”

Section: Ch 2 (E) = Ch 2 (T X)mentioning

confidence: 99%

“…One of the first examples of a heterotic quantum cohomology ring 14 considered in [1][section 6.2] concerns a heterotic theory on P 1 × P 1 , with gauge bundle given by a deformation of the tangent bundle. Recall that we can describe the tangent bundle of P 1 × P 1 as the cokernel of the map…”

Section: Physical Prediction For Quantum Cohomologymentioning

confidence: 99%

“…We shall describe how to generalize the rational-curve-counting of type II theories to generalizations of the 27 3 coupling in heterotic strings. We shall also check some of the predictions made recently in [1].…”

Section: Introductionmentioning

confidence: 99%

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Notes on Certain (0,2) Correlation Functions

Katz

Sharpe

2005

Commun. Math. Phys.

249

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In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations. Ordinary quantum chiral rings reflect worldsheet instanton corrections to correlation functions involving products of elements of Dolbeault cohomology groups on the target space. The heterotic generalization described here involves computing worldsheet instanton corrections to correlation functions defined by products of elements of sheaf cohomology groups. One must not only compactify moduli spaces of rational curves, but also extend a sheaf (determined by the gauge bundle) over the compactification, and linear sigma models provide natural mechanisms for doing both. Euler classes of obstruction bundles generalize to this language in an interesting way.

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Section: Stable Maps and Compactificationsmentioning

confidence: 99%

Section: Ch 2 (E) = Ch 2 (T X)mentioning

confidence: 99%

Section: Ch 2 (E) = Ch 2 (T X)mentioning

confidence: 99%

Section: Physical Prediction For Quantum Cohomologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Notes on Certain (0,2) Correlation Functions

Katz

Sharpe

2005

Commun. Math. Phys.

249

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Heterotic orbifold resolutions as (2,0) gauged linear sigma models

Nibbelink

2011

Fortschritte der Physik

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In this work we attempt to bridge the gap between heterotic orbifold models and Calabi-Yau compactifications using gauged linear sigma models (GLSMs) with (2,0) worldsheet supersymmetry. We associate a specific GLSM to a heterotic orbifold model with twisted states that have non-vanishing vacuum expectation values (VEVs): The charges of the GLSM superfields are essentially determined by the shifted momenta of these states. When a twisted state contains an oscillator excitation, a fermionic gauging is introduced on the worldsheet inducing a non-Abelian gauge bundle, e.g. the standard embedding. However, irrespectively of whether the twisted states contain oscillators or not, they can be interpreted as blow-up modes, as their VEVs are correlated with sizes of exceptional cycles in the resolved geometry. By considering marginal deformations of a GLSM in the large volume limit we are able to directly determine its effective four dimensional spectrum. In the cases considered the spectra coincide with those computed via index theorems.Comment: 4 pages, 10 figures, some typos corrected and mirror clarifications adde

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Landau-Ginzburg Theories

Melnikov

2019

An Introduction to Two-Dimensional Quantum Field Theory With (0,2) Supersymmetry

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(0,2) Duality

Cited by 81 publications

References 38 publications

Notes on Certain (0,2) Correlation Functions

Notes on Certain (0,2) Correlation Functions

Heterotic orbifold resolutions as (2,0) gauged linear sigma models

Landau-Ginzburg Theories

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