Overview Of K-Theory Applied To Strings

TL;DR

This paper reviews how K-theory classifies D-brane charges in string theory, extending to noncommutative algebras, and discusses implications for string field theory at infinite brane numbers.

Contribution

It highlights the role of K-theory in string theory, especially for noncommutative cases and the significance of infinite D-brane sets in string field theory.

Findings

K-theory classifies RR charges and fields in string theory.

Extension of K-theory to noncommutative algebras is natural for certain string models.

Infinite D-brane configurations are crucial for understanding tachyon condensation.

Abstract

K-theory provides a framework for classifying Ramond-Ramond (RR) charges and fields. K-theory of manifolds has a natural extension to K-theory of noncommutative algebras, such as the algebra considered in noncommutative Yang-Mills theory or in open string field theory. In a number of concrete problems, the K-theory analysis proceeds most naturally if one starts out with an infinite set of D-branes, reduced by tachyon condensation to a finite set. This suggests that string field theory should be reconsidered for N=infinity.