## 18 Citations

Quasi-periodic paths and a string 2-group model from the free loop group

- Mathematics
- 2017

In this paper we address the question of the existence of a model for the string 2-group as a strict Lie-2-group using the free loop group $LSpin$ (or more generally $LG$ for compact simple…

Principal ∞-bundles - General theory

- Mathematics
- 2012

The theory of principal bundles makes sense in any ∞-topos, such as the ∞-topos of topological, of smooth, or of otherwise geometric ∞-groupoids/∞-stacks, and more generally in slices of these. It…

A global perspective to connections on principal 2-bundles

- MathematicsForum Mathematicum
- 2018

For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action…

The Spinor Bundle on Loop Space and its Fusion product

- Mathematics
- 2020

Given a manifold with a string structure, we construct a spinor bundle on its loop space. Our construction is in analogy with the usual construction of a spinor bundle on a spin manifold, but…

Connes fusion of spinors on loop space

- Mathematics
- 2020

The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the…

Spin structures on loop spaces that characterize string manifolds

- Mathematics
- 2012

Classically, a spin structure on the loop space of a manifold is a lift of the structure group of the looped frame bundle from the loop group to its universal central extension. Heuristically, the…

Non-abelian gerbes and some applications in string theory

- Mathematics
- 2018

We review a systematic construction of the 2-stack of bundle gerbes via descent, and extend it to non-abelian gerbes. We review the role of non-abelian gerbes in orientifold sigma models, for the…

## References

SHOWING 1-10 OF 42 REFERENCES

Connections on non-abelian Gerbes and their Holonomy

- Mathematics
- 2008

We introduce an axiomatic framework for the parallel transport of connections on gerbes. It incorporates parallel transport along curves and along surfaces, and is formulated in terms of gluing…

Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories

- Mathematics
- 2005

We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal G-bundle with connection and a class in H4(BG, ℤ) for a compact semi-simple Lie…

Loop Spaces, Characteristic Classes and Geometric Quantization

- Mathematics
- 1994

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Recent developments in mathematical…

Central extensions of smooth 2–groups and a finite-dimensional string 2–group

- Mathematics
- 2011

We provide a model of the String group as a central extension of finite-dimensional 2‐groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps. This bicategory is a…

From loop groups to 2-groups

- Mathematics
- 2005

We describe an interesting relation between Lie 2-algebras, the Kac– Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where…

A LOOP SPACE FORMULATION FOR GEOMETRIC LIFTING PROBLEMS

- MathematicsJournal of the Australian Mathematical Society
- 2011

Abstract We review and then combine two aspects of the theory of bundle gerbes. The first concerns lifting bundle gerbes and connections on those, developed by Murray and by Gomi. Lifting gerbes…

Some Stuff about the String Gerbe

- Mathematics
- 2006

Let G be a compact, simple and simply connected Lie group and let π : P → M be a principal G bundle over a smooth manifold M . Let ν denote the universally transgressive generator ofH(G; Z) = Z and…

FOUR EQUIVALENT VERSIONS OF NONABELIAN GERBES

- Mathematics
- 2011

We recall and partially expand four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are…

Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection

- Mathematics
- 2010

We prove that the category of abelian gerbes with connection over a smooth manifold is equivalent to a certain category of principal bundles over the free loop space. These bundles are equipped with…