Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Joel Ekstrand; Reimundo Heluani; Maxim Zabzine

doi:10.1016/j.geomphys.2012.07.003

Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Joel Ekstrand^*, Reimundo Heluani, Maxim Zabzine

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We 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.

Original language	English (US)
Pages (from-to)	2259-2278
Number of pages	20
Journal	Journal of Geometry and Physics
Volume	62
Issue number	11
DOIs	https://doi.org/10.1016/j.geomphys.2012.07.003
State	Published - Nov 2012

Keywords

Poisson geometry
Poisson vertex algebra
SUSY vertex algebra
Vertex algebra

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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10.1016/j.geomphys.2012.07.003

Cite this

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title = "Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds",

abstract = "We 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.",

keywords = "Poisson geometry, Poisson vertex algebra, SUSY vertex algebra, Vertex algebra",

author = "Joel Ekstrand and Reimundo Heluani and Maxim Zabzine",

note = "Funding Information: M.Z. thanks KITP, Santa Barbara where part of this work was carried out. The research of M.Z. is supported by VR -grant 621-2008-4273 and is supported in part by DARPA under Grant No. HR0011-09-1-0015 and by the National Science Foundation under Grant No. PHY05-51164 . ",

year = "2012",

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doi = "10.1016/j.geomphys.2012.07.003",

language = "English (US)",

volume = "62",

pages = "2259--2278",

journal = "Journal of Geometry and Physics",

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TY - JOUR

T1 - Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

AU - Ekstrand, Joel

AU - Heluani, Reimundo

AU - Zabzine, Maxim

N1 - Funding Information: M.Z. thanks KITP, Santa Barbara where part of this work was carried out. The research of M.Z. is supported by VR -grant 621-2008-4273 and is supported in part by DARPA under Grant No. HR0011-09-1-0015 and by the National Science Foundation under Grant No. PHY05-51164 .

PY - 2012/11

Y1 - 2012/11

N2 - We 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.

AB - We 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.

KW - Poisson geometry

KW - Poisson vertex algebra

KW - SUSY vertex algebra

KW - Vertex algebra

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M3 - Article

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SN - 0393-0440

VL - 62

SP - 2259

EP - 2278

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 11

ER -

Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

Abstract

Keywords

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