Normal Coordinates in Kahler Manifolds and the Background Field Method | Zendy

Kiyoshi Higashijima | Zendy; Etsuko Itou | Zendy; Muneto Nitta | Zendy

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Normal Coordinates in Kahler Manifolds and the Background Field Method

Author(s) -

Kiyoshi Higashijima,

Etsuko Itou,

Muneto Nitta

Publication year - 2002

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.108.185

Subject(s) - holomorphic function , covariant transformation , physics , vector field , pure mathematics , field (mathematics) , tangent space , mathematical analysis , mathematical physics , mathematics , mechanics

Riemann normal coordinates (RNC) are unsuitable for \kahler manifolds sincethey are not holomorphic. Instead, \kahler normal coordinates (KNC) can bedefined as holomorphic coordinates. We prove that KNC transform as aholomorphic tangent vector under holomorphic coordinate transformations, andtherefore that they are natural extensions of RNC to the case of \kahlermanifolds. The KNC expansion provides a manifestly covariant background fieldmethod preserving the complex structure in supersymmetric nonlinear sigmamodels.Comment: LaTeX2e, 24 pages, no figures, the version to appear in Prog. Theor. Phys. 10

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