SUPERSYMMETRY AND GAUSS-BONNET-CHERN THEOREM

YU Yue

Chinese Physics C> 1988, Vol. 12> Issue(1) : 28-33

SUPERSYMMETRY AND GAUSS-BONNET-CHERN THEOREM

YU Yue ^,

Zhejiang University,Hangzhou

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Abstract：
Because the de Rham complex on compact manifolds with boundary must satify the elliptic boundary conditions,their boundary metric must be a product if the structures of supersymmetry satifying the conditions exist in the field manifolds with boundary on 0+1 dimensions.Using the witten index for a supersymmetric field theory,we proved the Gauss-Bonnet-Chern theorem.

References

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E. Witten, Nucl. Phys., B202(1982), 253.[2] E. Witten, J. Diff. Geom., 17(1982), 667.[3] E. Witten, Holomorphic morse inequalities, Priceton Preprint (1982).[4] L. Alvarez-Gzmme, Commun. Math. Phys., 90(1983), 161.[5] P. Windey, CERN Preprint TH3758(1983).[6] E. Getzler, Commun. Mazh. Phys., 92(1983), 163.[7] I. M. Bismat, Orsay Preprint (1983).[8] B. Zumino, LBL Preprint 17972(1982).[9] E. Witten, Phys. Rev., D16(1977), 2991.[10] P. Divecchia and S. Ferrara, Nucl. Phys., B130(1977), 93.[11] D. 2. Freedman and P. K. Townsend, Nucl. Phys., B177(1981), 282.[12] M. F. Atiyah and R. Bott, Diff. Analysis (Bombay Colloquium), Oxford, London (1964).[13] P. B. Gilkey, Adv. Math., 15(1975), 334.[14] S. Cecotti and L. Girardello, Phys. Lett., B110(1982), 39.[15] S. S. Chern, Ann. Math., 46(1942), 46.

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YU Yue. SUPERSYMMETRY AND GAUSS-BONNET-CHERN THEOREM[J]. Chinese Physics C, 1988, 12(1): 28-33.

YU Yue. SUPERSYMMETRY AND GAUSS-BONNET-CHERN THEOREM[J]. Chinese Physics C, 1988, 12(1): 28-33. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

SUPERSYMMETRY AND GAUSS-BONNET-CHERN THEOREM

YU Yue ^,

Corresponding author: YU Yue,

Zhejiang University,Hangzhou

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1988-02-05

Abstract: Because the de Rham complex on compact manifolds with boundary must satify the elliptic boundary conditions,their boundary metric must be a product if the structures of supersymmetry satifying the conditions exist in the field manifolds with boundary on 0+1 dimensions.Using the witten index for a supersymmetric field theory,we proved the Gauss-Bonnet-Chern theorem.