Abstract not found

ABSTRACT. – In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S 1-gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity, and the product structure K i α ⊗K j β → Ki+j α+β are derived. Our approach provides a uniform framework for studying various twisted K-theories including the usual twisted K-theory of topological spaces, twisted equivariant K-theory, and the twisted K-theory of orbifolds. We also present a Fredholm picture, and discuss the conditions under which twisted K-groups can be expressed by so-called “twisted vector bundles”. Our approach is to work on presentations of stacks, namely groupoids, and relies heavily on the machinery of K-theory (KK-theory) of C ∗-algebras. © 2004 Elsevier SAS RÉSUMÉ. – Dans cet article, nous développons la K-théorie tordue pour les champs différentiables, où la torsion s’effectue par une S 1-gerbe sur le champ en question. Nous en établissons les propriétés générales telles que les suites exactes de Mayer–Vietoris, la périodicité de Bott, et le produit K i α ⊗ K j β → Ki+j α+β. Notre approche fournit un cadre général permettant d’étudier diverses K-théories tordues, en particulier la K-théorie tordue usuelle des espaces topologiques, la K-théorie tordue équivariante, et la K-théorie tordue des orbifolds. Nous donnons également une définition équivalente utilisant des opérateurs de Fredholm, et nous discutons les conditions sous lesquelles les groupes de K-théorie tordue peuvent être réalisés à partir de “fibrés vectoriels tordus”. Notre approche consiste à travailler sur les réalisations concrètes des champs, à savoir les groupoïdes, et s’appuie de façon importante sur les techniques de K-théorie (KK-théorie) des C ∗-algèbres.

Abstract not found

I determine the twisted K–theory of all compact simply connected simple Lie groups. The computation reduces via the Freed–Hopkins–Teleman theorem [1] to the CFT prescription, and thus explains why it gives the correct result. Finally I analyze the exceptions noted by Bouwknegt et al [2].CONTENTS 1

We show that one can construct D-branes in parafermionic and WZW theories (and their orbifolds) which have very natural geometrical interpretations, and yet are not automatically included in the standard Cardy construction of D-branes in rational conformal field theory. The relation between these theories and their T-dual description leads to an analogy between these D-branes and the familiar A-branes and B-branes of N = 2 theories. May

Abstract. Twisted K-theory has received much attention recently in both mathematics and physics. We describe some models of twisted K-theory, both topological and geometric. Then we state a theorem which relates representations of loop groups to twisted equivariant K-theory. This is joint work with Michael Hopkins and Constantin Teleman. The loop group of a compact Lie group G is the space of smooth maps S 1 → G with multiplication defined pointwise. Loop groups have been around in topology for quite some time [Bo], and in the 1980s were extensively studied from the point of view of representation theory [Ka], [PS]. In part this was driven by the relationship to conformal field theory. The interesting representations of loop groups are projective, and with fixed projective cocycle τ there is a finite number of irreducible representations up to isomorphism. Considerations from conformal field theory [V] led to a ring structure on the abelian group R τ (G) they generate, at least for transgressed twistings. This is the Verlinde ring. For G simply connected R τ (G) is a quotient of the representation ring of G, but that is not true in general. At about this time Witten [W] introduced a three-dimensional topological quantum field theory in which the Verlinde ring plays an important role. Eventually it was understood that the fundamental object in that theory is a “modular tensor category ” whose Grothendieck group is the Verlinde ring. Typically it is a category of representations of a loop group or quantum group. For the special case of a finite group G the topological field theory is specified by a certain

Abstract. In this paper we compute the charge group for symmetry preserving D-branes

We present an encompassing treatment of D–brane charges in supersymmetric SO(3) WZW models. There are two distinct supersymmetric CFTs at each even level: the standard bosonic SO(3) modular invariant tensored with free fermions, as well as a novel twisted model. We calculate the relevant twisted K–theories and find complete agreement with the CFT analysis of D–brane charges. The K–theoretical computation in particular elucidates some important aspects of N = 1 supersymmetric WZW models on non-simply connected Lie groups. March 2004Contents 1

Abstract. In this paper we construct an explicit geometric model for the group of gerbes over an orbifold X. We show how from its curvature we can obtain its characteristic class in H 3 (X) via Chern-Weil theory. For an arbitrary gerbe L, a twisting L Korb(X) of the orbifold K-theory of X is constructed, and shown to generalize previous twisting by Rosenberg [28], Witten [35], Atiyah-Segal [2] and Bowknegt et. al. [4] in the smooth case and by Adem-Ruan [1] for discrete torsion on an orbifold. Contents

Abstract not found