Related papers: p-Gerbes and Extended Objects in String Theory
We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of $\Z_p$ gauge theories shows that they are associated with an…
If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher…
We make the category BGrb_M of bundle gerbes on a manifold M into a 2-category by providing 2-cells in the form of transformations of bundle gerbe morphisms. This description of BGrb_M as a 2-category is used to define the notion of a…
We use bundle gerbes and their connections and curvings to obtain an explicit formula for a de Rham representative of the string class of a loop group bundle. This is related to earlier work on calorons.
In addition to being a prime candidate for a fundamental unified theory of all interactions in nature, string theory provides a natural setting to understand gauge field theories. This is linked to the concept of "D-branes": extended,…
String-string duality dictates that type IIA strings compactified on a K3 surface acquire non-abelian gauge groups for certain values of the K3 moduli. We argue that, contrary to expectation, the theories for which such enhanced gauge…
We argue that a description of supersymmetric extended objects from a unified geometric point of view requires an enlargement of superspace. To this aim we study in a systematic way how superspace groups and algebras arise from Grassmann…
This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of…
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with $1\le p\le D$, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell…
Algebraic parabolic bundles on smooth projective curves over algebraically closed field of positive characteristic is defined. It is shown that the category of algebraic parabolic bundles is equivalent to the category of orbifold bundles…
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools come from the well-known de Rham-Kodaira decomposing theorem on the harmonic…
In this article, we study how the Grothendieck group of coherent sheaves can be used to describe D-branes. We show how global bound state construction in topological $K$-theory can be adapted to our context, showing that D-branes wrapping a…
We report on the gauged supergravity interpretation of certain compactifications of superstring theories with p-form fluxes turned on. We discuss in particular the interplay of duality symmetries in type IIB orientifolds and gauged…
In this series of lectures I present a review of the geometric structures of supergravity in diverse dimensions mostly relevant to p-brane physics and to pinpoint the correspondence between the macroscopic and microscopic description of…
In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group in terms of representation rings of subgroups of its Sylow. We also prove a stable elements…
We extend the notion of a {$p$-permutation equivalence} between two $p$-blocks $A$ and $B$ of finite groups $G$ and $H$, from the definition in [Boltje-Xu 2008] to a virtual $p$-permutation bimodule whose components have twisted diagonal…
In the paper arXiv:0810.4291 we have shown, in the context of type II superstring theory, the classification of the allowed B-field and A-field configurations in the presence of anomaly-free D-branes, the mathematical framework being…
Recently twisted K-theory has received much attention due to its applications in string theory and the announced result by Freed, Hopkins and Telemann relating the twisted equivariant K-theory of a compact Lie group to its Verlinde algebra.…
We continue to study 5d N=1 supersymmetric field theories and their compactifications on a circle through brane configurations. We develop a model, which we call (p,q) Webs, which enables simple geometrical computations to reproduce the…
Abelian gerbes and twisted bundles describe the topology of the NS-NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted…