Edward Witten discusses how D-brane charge takes values in the K-theory of spacetime, based on recent arguments about stable nonsupersymmetric D-brane states. He argues that D-brane charges are better understood in terms of K-theory rather than cohomology, as K-theory involves vector bundles and gauge fields, which are more relevant to D-branes. He also describes new objects such as a -1-brane in Type I superstring theory. The paper explores the relationship between D-brane charges and K-theory, showing that the methods used in analyzing the brane-antibrane system lead naturally to the identification of D-brane charge as an element of K(X), the K-theory of the spacetime manifold X. The paper also discusses the implications of this for various string theories, including Type I, Type IIA, and Type IIB, and how brane-antibrane annihilation relates to K-theory. The paper concludes that D-brane charges are classified by K-theory, with the understanding that the precise version of K(X) depends on the specific situation.Edward Witten discusses how D-brane charge takes values in the K-theory of spacetime, based on recent arguments about stable nonsupersymmetric D-brane states. He argues that D-brane charges are better understood in terms of K-theory rather than cohomology, as K-theory involves vector bundles and gauge fields, which are more relevant to D-branes. He also describes new objects such as a -1-brane in Type I superstring theory. The paper explores the relationship between D-brane charges and K-theory, showing that the methods used in analyzing the brane-antibrane system lead naturally to the identification of D-brane charge as an element of K(X), the K-theory of the spacetime manifold X. The paper also discusses the implications of this for various string theories, including Type I, Type IIA, and Type IIB, and how brane-antibrane annihilation relates to K-theory. The paper concludes that D-brane charges are classified by K-theory, with the understanding that the precise version of K(X) depends on the specific situation.