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

SUPERSYMMETRY AND GAUSS-BONNET-CHERN THEOREM

YU Yue^,

Zhejiang University,Hangzhou

Abstract
HTML
Reference
Related

PDF

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

[1]

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.

[1]	F. dos Anjos,M. Novello. Friedmann’s universe controlled by Gauss-Bonnet modified gravity. Chinese Physics C, 2025, 49(4): 045108.doi:10.1088/1674-1137/ad9b9e
[2]	Wen-Bin Chang,De-fu Hou. Holographic Schwinger effect in an anisotropic background with Gauss-Bonnet corrections. Chinese Physics C, 2023, 47(11): 114105.doi:10.1088/1674-1137/acf7b6
[3]	Cai-Ying Shao,Yu Hu,Cheng-Gang Shao. Parameter estimation for Einstein-dilaton-Gauss-Bonnet gravity with ringdown signals. Chinese Physics C, 2023, 47(10): 105101.doi:10.1088/1674-1137/ace522
[4]	Tong-Zheng Wang,Wei-Liang Qian,Juan Fernando Zapata Zapata,Kai Lin. Scalar and Dirac quasinormal modes of scalar-tensor-Gauss-Bonnet black holes. Chinese Physics C, 2022, 46(4): 045101.doi:10.1088/1674-1137/ac3d29
[5]	Yunlong Liu,Xiangdong Zhang. Collisional Penrose process of 4D rotational Einstein-Gauss-Bonnet black holes. Chinese Physics C, 2021, 45(5): 055102.doi:10.1088/1674-1137/abe36a
[6]	Ming Zhang,Chao-Ming Zhang,De-Cheng Zou,Rui-Hong Yue. Phase transition and quasinormal modes for charged black holes in 4D Einstein-Gauss-Bonnet gravity. Chinese Physics C, 2021, 45(4): 045105.doi:10.1088/1674-1137/abe19a
[7]	H. Lü,Pujian Mao. Asymptotic structure of Einstein-Gauss-Bonnet theory in lower dimensions. Chinese Physics C, 2021, 45(1): 013110.doi:10.1088/1674-1137/abc23f
[8]	Julio Arrechea,Adrià Delhom,Alejandro Jiménez-Cano. Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity. Chinese Physics C, 2021, 45(1): 013107.doi:10.1088/1674-1137/abc1d4
[9]	Shuxuan Ying. Thermodynamics and weak cosmic censorship conjecture of 4D Gauss-Bonnet-Maxwell black holes via charged particle absorption. Chinese Physics C, 2020, 44(12): 125101.doi:10.1088/1674-1137/abb4c9
[10]	Hong Ma,Jin Li. Gravitational quasinormal modes of static Einstein-Gauss-Bonnet anti-de Sitter black holes. Chinese Physics C, 2018, 42(4): 045101.doi:10.1088/1674-1137/42/4/045101
[11]	HUO Qiu-Hong,JIANG Yun-Guo,WANG Ru-Zhi,YAN Hui. Anomalous spin of the Chern-Simons-Georgi-Glashow model. Chinese Physics C, 2013, 37(4): 043104.doi:10.1088/1674-1137/37/4/043104
[12]	WANG Ke,JIANG Yun-Guo,HUO Qiu-Hong. Quantal symmetries in the non-linear σ model with Maxwell and non-Abelian Chern-Simons terms. Chinese Physics C, 2010, 34(5): 535-538.doi:10.1088/1674-1137/34/5/003
[13]	WANG Yong-Long,LI Zi-Ping. Symmetries in the Non-linear Sigma Model with Maxwell-Chern-Simons Term. Chinese Physics C, 2004, 28(7): 696-698.
[14]	LONG Zheng-Wen,LIU Bo,LI Zi-Ping. Canonical Quantization of the Complex Scalar Field Coupled to the Abel Chern-Simons Term. Chinese Physics C, 2003, 27(10): 866-869.
[15]	LI Rui-Jie,LI Zi-Ping. Quantal Canonical Symmetries in Spinor QED with Chern-Simons Term. Chinese Physics C, 2002, 26(4): 325-330.
[16]	Jiang Jinhuan,Li Ziping. Quantization of a Scalar QED With Chern-Simons Term in the Batalin-Fradkin-Vilkovisky Scheme. Chinese Physics C, 1999, 23(8): 784-789.
[17]	Zhang Zhihe,Li Ziping. Casimir Effect of the Maxwell- Chern-Simons Field. Chinese Physics C, 1998, 22(1): 87-91.
[18]	Guo Shuohong,Fang Xiyan. Quantization of Lattice Chern-Simons Theory. Chinese Physics C, 1994, 18(8): 706-714.
[19]	Yu Yue. Supersymmetry and The Gauss-Bonnet-Chern Theorem. Chinese Physics C, 1988, 12(S2): 123-130.
[20]	ZHOU Guang-Zhao,WU Yue-Liang,XIE Yan-Bo. THE GENERAL CHERN-SIMONS COCHAIN AND THEIR APPLICATION. Chinese Physics C, 1986, 10(2): 177-185.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(3705)
PDF Downloads(469)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者:陈斌, bchen63@163.com

1.
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.