Non-linear sigma models via the chiral de Rham complex

Ekstrand, Joel; Heluani, Reimundo; Kallen, Johan; Zabzine, Maxim

doi:10.48550/arxiv.0905.4447

Cited by 4 publications

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“…To do this, we consider the classical supersymmetric sigma model, and we derive a Hamiltonian formulation thereof. A similar treatment of the N = 1 sigma model was initiated in [13,14] and its relation to CDR was suggested in [7]. Here, we suggest the similar relation between the N = (2, 2) supersymmetric sigma models with a Calabi-Yau target and the sheaf of N = 2 supersymmetric vertex algebras on the same Calabi-Yau.…”

Section: N = (2 2) Vertex Algebra On a Calabi-yau Manifoldsupporting

confidence: 70%

“…The N = 2 sheaf can be related to the Chiral de Rham complex (the sheaf of N = 1 SUSY vertex algebras associated to the standard Courant algebroid on T M ⊕ T * M ). It is instructive to expand the superfield Φ in such way so we make contact with previous [3,2,7] calculations. Let φ µ (z, θ 1 ) be an even N = 1 superfield, and S ν (z, θ 1 ) an odd N = 1 superfield with the expansions…”

Section: Relation To the Chiral De Rham Complexmentioning

confidence: 99%

“…The expression (6.3) is the classical version of the operator H considered in (5.7). Thus, following the logic presented in [7], we can think of the sheaf of N = 2 supersymmetric vertex algebras on a Calabi-Yau as a formal quantization of the N = (2, 2) sigma model defined by the action (6.1).…”

Section: N = (2 2) Vertex Algebra On a Calabi-yau Manifoldmentioning

confidence: 99%

“…There is a quasiclassical version of CDR as a sheaf of Poisson vertex algebras [6]. This can be naturally related to the Hamiltonian treatment of supersymmetric classical non-linear sigma models [7]. Indeed, CDR can be interpreted as a formal quantization of the non-linear sigma model.…”

Section: Introductionmentioning

confidence: 99%

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Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Ekstrand

Heluani

Zabzine

2012

Journal of Geometry and Physics

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a b s t r a c tWe construct a sheaf of N = 2 vertex algebras naturally associated to any Poisson manifold.The relation of this sheaf to the chiral de Rham complex is discussed. We reprove the result about the existence of two commuting N = 2 superconformal structures on the space of sections of the chiral de Rham complex of a Calabi-Yau manifold, but now calculated in a manifest N = 2 formalism. We discuss how the semi-classical limit of this sheaf of N = 2 vertex algebras is related to the classical supersymmetric non-linear sigma model.

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Section: N = (2 2) Vertex Algebra On a Calabi-yau Manifoldsupporting

confidence: 70%

Section: Relation To the Chiral De Rham Complexmentioning

confidence: 99%

Section: N = (2 2) Vertex Algebra On a Calabi-yau Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Ekstrand

Heluani

Zabzine

2012

Journal of Geometry and Physics

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“…In the physics literature, CDR appeared in the context of half-twisted sigma models [5,6] and in the context of infinite volume limits of sigma models [7,8,9]. The present work is the logical continuation of [10], where it was suggested to interpret CDR as a formal canonical quantization of the non-linear sigma model.…”

Section: Introductionmentioning

confidence: 82%

Chiral de Rham Complex on Riemannian Manifolds and Special Holonomy

Ekstrand

Heluani

Kallen

et al. 2013

Commun. Math. Phys.

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Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We show how to systematically construct global sections of CDR from differential forms, and investigate the algebra of the sections corresponding to the covariantly constant forms associated with the special holonomy. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N = 2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau threefold and conjecture similar results for G 2 manifolds. We also discuss quasi-classical limits of these algebras.

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A worldsheet theory for supergravity

Adamo

Casali

Skinner

2015

J. High Energ. Phys.

131

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We present a worldsheet theory that describes maps into a curved target space equipped with a B-field and dilaton. The conditions for the theory to be consistent at the quantum level can be computed exactly, and are that the target space fields obey the nonlinear d = 10 supergravity equations of motion, with no higher curvature terms. The path integral is constrained to obey a generalization of the scattering equations to curved space. Remarkably, the supergravity field equations emerge as quantum corrections to these curved space scattering equations.

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Non-linear sigma models via the chiral de Rham complex

Cited by 4 publications

References 0 publications

Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Chiral de Rham Complex on Riemannian Manifolds and Special Holonomy

A worldsheet theory for supergravity

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