group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
What is called self-conjugate K-theory of spaces $X$ (Anderson 64) is KR-theory on real spaces of the form $X \times S^{0,2}$, where the second factor denotes the circle equipped with the antipodal $\mathbb{Z}_2$-action (see at real space for the notation).
In the context of type II string theory on orientifolds $KSC$-theory is the cohomology theory in which the RR-fields of the $\tilde I$-variant of type I superstring theory are cocycles (Witten 98, DMR 13, section 3.3.)
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 $KU^1$ |
type IIB superstring | super line 2-bundle | $B GL_1(KU)$ | KU-theory $KU^0$ |
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 $KSC$ |
The definition of KSc theory is due to
Discussion of applications to superstring theory on orientifolds is in
Edward Witten, section 5 of D-branes and K-theory, J. High Energy Phys., 1998(12):019, 1998 (arXiv:hep-th/9810188)
Charles Doran, Stefan Mendez-Diez, Jonathan Rosenberg, T-duality For Orientifolds and Twisted KR-theory (arXiv:1306.1779)
Last revised on December 8, 2015 at 16:10:11. See the history of this page for a list of all contributions to it.