Supersymmetry of the chiral de Rham complex 2: Commuting sectors

Reimundo Heluani

doi:10.1093/imrn/rnn145

Supersymmetry of the chiral de Rham complex 2: Commuting sectors

Reimundo Heluani^*

^*Corresponding author for this work

Mathematics

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

19 Scopus citations

Abstract

We construct two commuting N = 2 structures on the space of sections of the chiral de Rham complex (CDR) of a Calabi-Yau manifold. We use this extra supersymmetry to construct a nonlinear automorphism of CDR preserving these N = 2 structures. Finally, we show how to extend these results to construct a commuting pair of N = 4 super vertex algebras in the HyperKähler case.

Original language	English (US)
Pages (from-to)	953-987
Number of pages	35
Journal	International Mathematics Research Notices
Volume	2009
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnn145
State	Published - 2009

ASJC Scopus subject areas

General Mathematics

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title = "Supersymmetry of the chiral de Rham complex 2: Commuting sectors",

abstract = "We construct two commuting N = 2 structures on the space of sections of the chiral de Rham complex (CDR) of a Calabi-Yau manifold. We use this extra supersymmetry to construct a nonlinear automorphism of CDR preserving these N = 2 structures. Finally, we show how to extend these results to construct a commuting pair of N = 4 super vertex algebras in the HyperK{\"a}hler case.",

author = "Reimundo Heluani",

note = "Funding Information: thank E. Frenkel for numerous explanations—including the suggestion of complexifying the K{\"a}hler form; M. Aldi and A. Linshaw for interesting discussions; and M. Szczesny for his generosity in sharing his insights. This work was supported by the Miller Institute for Basic Research in Science.",

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doi = "10.1093/imrn/rnn145",

language = "English (US)",

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N1 - Funding Information: thank E. Frenkel for numerous explanations—including the suggestion of complexifying the Kähler form; M. Aldi and A. Linshaw for interesting discussions; and M. Szczesny for his generosity in sharing his insights. This work was supported by the Miller Institute for Basic Research in Science.

PY - 2009

Y1 - 2009

N2 - We construct two commuting N = 2 structures on the space of sections of the chiral de Rham complex (CDR) of a Calabi-Yau manifold. We use this extra supersymmetry to construct a nonlinear automorphism of CDR preserving these N = 2 structures. Finally, we show how to extend these results to construct a commuting pair of N = 4 super vertex algebras in the HyperKähler case.

AB - We construct two commuting N = 2 structures on the space of sections of the chiral de Rham complex (CDR) of a Calabi-Yau manifold. We use this extra supersymmetry to construct a nonlinear automorphism of CDR preserving these N = 2 structures. Finally, we show how to extend these results to construct a commuting pair of N = 4 super vertex algebras in the HyperKähler case.

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 6

ER -

Supersymmetry of the chiral de Rham complex 2: Commuting sectors

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