A-twisted Landau–Ginzburg models

Guffin, Josh; Sharpe, Eric

doi:10.1016/j.geomphys.2009.07.014

Cited by 39 publications

(61 citation statements)

References 37 publications

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“…Working in a geometric phase, we find that under the twist φ 0 becomes a holomorphic one-form on the worldsheet, denoted by φ 0 z , whose kinetic term has no zero modes on a genus zero world-sheet. Details of this aspect of the twist have been worked out recently in [29].…”

Section: A-twist Of the M-model: Quantum Restrictionmentioning

confidence: 99%

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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-twist Of the M-model: Quantum Restrictionmentioning

confidence: 99%

“…As in [10,29] a Hermitian metric on O(d i ) → P 1 has been used in some of the definitions, so that the sections of the bundles in braces count zero modes of the kinetic operator in a fixed instanton background. Under this twist the supercharge Q + becomes the nilpotent world-sheet scalar operator Q T .…”

Section: The A/2 Twistmentioning

confidence: 99%

Summing the instantons in half-twisted linear sigma models

McOrist

Melnikov

2009

J. High Energy Phys.

122

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“…In our recent paper [11], we discussed the A twist of (2, 2) Landau-Ginzburg models, which has only rarely been discussed in the literature before. In this paper, we extend the analysis of [11] to consider (pseudo-)topological A, B twists of (0, 2) Landau-Ginzburg models, closely analogous to the A, B (0, 2) twists of nonlinear sigma models (NLSMs) discussed in [2-6, 9,10].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we extend the analysis of [11] to consider (pseudo-)topological A, B twists of (0, 2) Landau-Ginzburg models, closely analogous to the A, B (0, 2) twists of nonlinear sigma models (NLSMs) discussed in [2-6, 9,10].…”

Section: Introductionmentioning

confidence: 99%

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A-twisted heterotic Landau–Ginzburg models

Guffin

Sharpe

2009

Journal of Geometry and Physics

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a b s t r a c tIn this paper, we apply the methods developed in recent work for constructing A-twisted (2, 2) Landau-Ginzburg models to analogous (0, 2) models. In particular, we study (0, 2) Landau-Ginzburg models on topologically non-trivial spaces away from large-radius limits, where one expects to find correlation function contributions akin to (2, 2) curve corrections. Such heterotic theories admit A-and B-model twists, and exhibit a duality that simultaneously exchanges the twists and dualizes the gauge bundle. We explore how this duality operates in heterotic Landau-Ginzburg models, as well as other properties of these theories, using examples which renormalization-group flow to heterotic nonlinear sigma models as checks on our methods.

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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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A-twisted Landau–Ginzburg models

Cited by 39 publications

References 37 publications

Summing the instantons in half-twisted linear sigma models

Summing the instantons in half-twisted linear sigma models

A-twisted heterotic Landau–Ginzburg models

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

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