Advances in Theoretical and Mathematical Physics

Volume 27 (2023)

Number 2

Differential $KO$-theory via gradations and mass terms

Pages: 381 – 481



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

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


We construct models of the differential $KO$-theory and the twisted differential $KO$-theory, by refining Karoubi’s $KO$-theory $\href{}{[Kar78]}$ 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 $\href{}{[Qui85]}$. One of our models can be regarded as classifying “fermionic mass terms” in physics.

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