Twisted differential K-theory is the twisted differential cohomology version K-theory: the combination of differential K-theory and twisted K-theory.
Roughly this is an extension of twisted de Rham cohomology by twisted K-theory via the twisted Chern character map.
To the extent that D-brane charge is classified by K-theory (see there), it is twisted differential K-theory that is relevant: the differential aspect captures the higher gauge field called the RR-field, and the twisted aspects captures the higher gauge field called the B-field, in string theory.
This example of D-brane charge used to be one of the main motivations for finding a definition and construction of twisted differential cohomology theories. Earlier articles on D-brane charge had to assume that such a theory exists (e.g. DFM 09). Actual models now exist (Grady-Sati 19a, Grady-Sati 19b)
Preliminary discussion included
Alan Carey, Differential twisted K-theory and applications , ESI preprint (pdf)
Alexander Kahle, Alessandro Valentino, T-Duality and Differential K-Theory
and specifically the need for twisted differential K-theory for the description of type II string theory backgrounds with their RR-fields and B-fields on orientifolds was highlighted in
Actual constructions appear with
Review in
A definition and proof of its pertinent properties of twisted differential cohomology in general and of twisted differential K-theory in particular is due to
See also:
More detailed discussion of twisted differential K-theory for KU/KO and its application to K-theory classification of D-brane charge:
Daniel Grady, Hisham Sati, Ramond-Ramond fields and twisted differential K-theory (arXiv:1903.08843)
Daniel Grady, Hisham Sati, Twisted differential KO-theory (arXiv:1905.09085)
Fabio Ferrari Ruffino, Juan Carlos Rocha Barriga, Twisted differential K-characters and D-branes, Nuclear Physics B Volume 960, November 2020, 115169 (arXiv:2009.04223. doi:10.1016/j.nuclphysb.2020.115169)
Last revised on March 8, 2021 at 14:42:20. See the history of this page for a list of all contributions to it.