2D sigma models and differential Poisson algebras

Cesar Arias, Nicolas Boulanger, Per Sundell, Alexander Torres-Gomez

Resultado de la investigación: Article

3 Citas (Scopus)

Resumen

Abstract: We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

Idioma originalEnglish
Número de artículo95
Páginas (desde-hasta)1-18
Número de páginas18
PublicaciónJournal of High Energy Physics
Volumen2015
N.º8
DOI
EstadoPublished - 1 ago 2015

Huella dactilar

algebra
operators
symmetry
brackets
products
supersymmetry
equations of motion
stars

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Citar esto

Arias, Cesar ; Boulanger, Nicolas ; Sundell, Per ; Torres-Gomez, Alexander. / 2D sigma models and differential Poisson algebras. En: Journal of High Energy Physics. 2015 ; Vol. 2015, N.º 8. pp. 1-18.
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2D sigma models and differential Poisson algebras. / Arias, Cesar; Boulanger, Nicolas; Sundell, Per; Torres-Gomez, Alexander.

En: Journal of High Energy Physics, Vol. 2015, N.º 8, 95, 01.08.2015, p. 1-18.

Resultado de la investigación: Article

TY - JOUR

T1 - 2D sigma models and differential Poisson algebras

AU - Arias, Cesar

AU - Boulanger, Nicolas

AU - Sundell, Per

AU - Torres-Gomez, Alexander

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N2 - Abstract: We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

AB - Abstract: We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

KW - Differential and Algebraic Geometry

KW - NonCommutative Geometry

KW - Topological Field Theories

KW - Topological Strings

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