The Noncommutative Residue about Witten Deformation
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In this paper, we compute lower dimensional volumes Vol 4 (1,1) and Vol 6 (2,2) about Witten deformation for 4, 6-dimensional spin manifolds with boundary respectively, and get assosiated Kastler–Kalau–Walze type theorems. We also give theoritic explaination of the gravitational action for 4, 6 dimensional manifolds with boundary by these noncommutative residues.
KeywordsLower-dimensional volumes noncommutative residue gravitational action Witten deformation
MR(2010) Subject Classification58G20 53A30 46L87
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This work is supported by Science Foundation for BS423 and Inner Mongolia Natural Science Foundation: No. 2018LHO1004. The author also thank the referee for his (or her) careful reading and helpful comments.
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