nLab string theory and cohomology theory -- table

cohomology theories of string theory fields on orientifolds

string theory	B-field	$B$-field moduli	RR-field
bosonic string	line 2-bundle	ordinary cohomology $H\mathbb{Z}^3$
type II superstring	super line 2-bundle	$Pic(KU)//\mathbb{Z}_2$	KR-theory $KR^\bullet$
type IIA superstring	super line 2-bundle	$B GL_1(KU)$	KU-theory $KU^0$
type IIB superstring	super line 2-bundle	$B GL_1(KU)$	KU-theory $KU^1$
type I superstring	super line 2-bundle	$Pic(KU)//\mathbb{Z}_2$	KO-theory $KO$
type $\tilde I$ superstring	super line 2-bundle	$Pic(KU)//\mathbb{Z}_2$	KSC-theory $KSC$