Combining an abelianized Yang-Mills field with its dual in 6D N=(1,0) supergravity yields a class in twisted K-theory, with the B-field as twist.
Twisted Morava K-theory and E-theory
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abstract
For an integral cohomology class H of degree n+2 on a space X, we define twisted Morava K-theory K(n)(X; H) at the prime 2, as well as an integral analogue. We explore properties of this twisted cohomology theory, study a twisted Atiyah-Hirzebruch spectral sequence, and give a universal coefficient theorem (in the spirit of Khorami). We extend the construction to define twisted Morava E-theory, and provide applications to string theory and M-theory.
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Six-dimensional gauge theories and (twisted) generalized cohomology
Combining an abelianized Yang-Mills field with its dual in 6D N=(1,0) supergravity yields a class in twisted K-theory, with the B-field as twist.