Making the hyper-Kähler structure of N = 2 quantum string manifest

Abstract

We show that the Lorentz covariant formulation of N = 2 string in a curved space reveals an explicit hyper-Kähler structure. Apart from the metric, the superconformal currents couple to a background two-form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.

Original language	English
Article number	024013
Journal	Physical Review D - Particles, Fields, Gravitation and Cosmology
Volume	70
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevD.70.024013
Publication status	Published - Jul 2004

ASJC Scopus subject areas

Physics and Astronomy(all)
Nuclear and High Energy Physics
Mathematical Physics

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10.1103/PhysRevD.70.024013

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title = "Making the hyper-K{\"a}hler structure of N = 2 quantum string manifest",

abstract = "We show that the Lorentz covariant formulation of N = 2 string in a curved space reveals an explicit hyper-K{\"a}hler structure. Apart from the metric, the superconformal currents couple to a background two-form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.",

author = "S. Bellucci and Galajinsky, {A. V.} and E. Latini",

year = "2004",

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AB - We show that the Lorentz covariant formulation of N = 2 string in a curved space reveals an explicit hyper-Kähler structure. Apart from the metric, the superconformal currents couple to a background two-form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.

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