16 research outputs found
Type I D-branes in an H-flux and twisted KO-theory
Witten has argued that charges of Type I D-branes in the presence of an
H-flux, take values in twisted KO-theory. We begin with the study of real
bundle gerbes and their holonomy. We then introduce the notion of real bundle
gerbe KO-theory which we establish is a geometric realization of twisted
KO-theory. We examine the relation with twisted K-theory, the Chern character
and provide some examples. We conclude with some open problems.Comment: 23 pages, Latex2e, 2 new references adde
D-branes, KK-theory and duality on noncommutative spaces
We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology, a refinement of open string T-duality, and a general criterion for cancellation of global worldsheet anomalies
Lectures on Nongeometric Flux Compactifications
These notes present a pedagogical review of nongeometric flux
compactifications. We begin by reviewing well-known geometric flux
compactifications in Type II string theory, and argue that one must include
nongeometric "fluxes" in order to have a superpotential which is invariant
under T-duality. Additionally, we discuss some elementary aspects of the
worldsheet description of nongeometric backgrounds. This review is based on
lectures given at the 2007 RTN Winter School at CERN.Comment: 31 pages, JHEP
The Ricci flow on noncommutative two-tori
In this paper we construct a version of Ricci flow for noncommutative 2-tori,
based on a spectral formulation in terms of the eigenvalues and eigenfunction
of the Laplacian and recent results on the Gauss-Bonnet theorem for
noncommutative tori.Comment: 18 pages, LaTe
Analysis of gauge-equivariant complexes and a topological index theorem for gauge-invariant families
‘Where do I belong?’
The Lichnerowicz formula yields an index theoretic obstruction to positive
scalar curvature metrics on closed spin manifolds. The most general form of
this obstruction is due to Rosenberg and takes values in the -theory of the
group -algebra of the fundamental group of the underlying manifold. We
give an overview of recent results clarifying the relation of the Rosenberg
index to notions from large scale geometry like enlargeability and
essentialness. One central topic is the concept of -homology classes of
infinite -area. This notion, which in its original form is due to Gromov, is
put in a general context and systematically used as a link between
geometrically defined large scale properties and index theoretic
considerations. In particular, we prove essentialness and the non-vanishing of
the Rosenberg index for manifolds of infinite -area.Comment: 23 pages, small changes and correction