Advances in Theoretical and Mathematical Physics

Volume 27 (2023)

Number 2

Differential $KO$-theory via gradations and mass terms

Pages: 381 – 481

DOI: https://dx.doi.org/10.4310/ATMP.2023.v27.n2.a1

Authors

Kiyonori Gomi (Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan)

Mayuko Yamashita (Department of Mathematics, Kyoto University, Sakyo-ku, Kyoto, Japan)

Abstract

We construct models of the differential $KO$-theory and the twisted differential $KO$-theory, by refining Karoubi’s $KO$-theory $\href{https://worldcat.org/title/1120894092}{[Kar78]}$ in terms of gradations on Clifford modules. In order for this, we set up the generalized Clifford superconnection formalism which generalizes the Quillen’s superconnection formalism $\href{https://doi.org/10.1016/0040-9383(85)90047-3}{[Qui85]}$. One of our models can be regarded as classifying “fermionic mass terms” in physics.

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K.G. is supported by JSPS KAKENHI Grant Numbers 20K03606 and JP17H06461.

M.Y. is supported by JSPS KAKENHI Grant Number 20K14307 and JST CREST program JPMJCR18T6.

Published 12 October 2023