# nLab KSC-theory

Contents

cohomology

### Theorems

#### Stable Homotopy theory

stable homotopy theory

Introduction

# Contents

#### Representation theory

representation theory

geometric representation theory

# Contents

## Idea

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).

## Applications

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 theoryB-field$B$-field moduliRR-field
bosonic stringline 2-bundleordinary cohomology $H\mathbb{Z}^3$
type II superstringsuper line 2-bundle$Pic(KU)//\mathbb{Z}_2$KR-theory $KR^\bullet$
type IIA superstringsuper line 2-bundle$B GL_1(KU)$KU-theory $KU^1$
type IIB superstringsuper line 2-bundle$B GL_1(KU)$KU-theory $KU^0$
type I superstringsuper line 2-bundle$Pic(KU)//\mathbb{Z}_2$KO-theory $KO$
type $\tilde I$ superstringsuper line 2-bundle$Pic(KU)//\mathbb{Z}_2$KSC-theory $KSC$

## References

The definition of KSc theory is due to

• D. W. Anderson, The real K-theory of classifying spaces Proc. Nat. Acad. Sci. U. S. A., 51(4):634–636, 1964.

Discussion of applications to superstring theory on orientifolds is in

Last revised on December 8, 2015 at 16:10:11. See the history of this page for a list of all contributions to it.