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Prog. Theor. Phys. Vol. 108 No. 1 (2002) pp. 185-202

[ Full Text PDF : FREE ACCESS (204K) ]

Normal Coordinates in Kähler Manifolds and the Background Field Method

Kiyoshi Higashijima,1,* Etsuko Itou1,** and Muneto Nitta2,***

1Department of Physics, Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan
2Department of Physics, Purdue University, West Lafayette, IN 47907-1396, USA

(Received March 18, 2002)

Abstract:

Riemann normal coordinates (RNC) are unsuitable for Kähler manifolds since they are not holomorphic. Instead, Kähler normal coordinates (KNC) can be defined as holomorphic coordinates. We prove that KNC transform as a holomorphic tangent vector under holomorphic coordinate transformations, and therefore that they are natural extensions of RNC to the case of Kähler manifolds. The KNC expansion provides a manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models.


URL : http://ptp.ipap.jp/link?PTP/108/185/
DOI : 10.1143/PTP.108.185


*E-mail: higashij@phys.sci.osaka-u.ac.jp
**E-mail: itou@het.phys.sci.osaka-u.ac.jp
***E-mail: nitta@physics.purdue.edu

[ Full Text PDF : FREE ACCESS (204K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 108 No. 4 (2002) pp. 737-753 :
    Wilsonian Renormalization Group Approach to N=2 Supersymmetric Sigma Models
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  2. Progress of Theoretical Physics Vol. 110 No. 1 (2003) pp. 107-114 :
    Unitarity Bound of the Wave Function Renormalization Constant
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  3. Progress of Theoretical Physics Vol. 110 No. 3 (2003) pp. 563-578 :
    Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method
    Kiyoshi Higashijima and Etsuko Itou
  4. Progress of Theoretical Physics Vol. 117 No. 6 (2007) pp. 1139-1156 :
    Three Dimensional Conformal Sigma Models
    Takeshi Higashi, Kiyoshi Higashijima and Etsuko Itou
  5. Progress of Theoretical Physics Supplement No.164 (2006) pp. 103-108 :
    Wilsonian Renormalization Approach to Nonlinear Sigma Models
    Takeshi Higashi, Kiyoshi Higashijima and Etsuko Itou

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