# Gerbes and Lie Groups

@article{Schweigert2011GerbesAL, title={Gerbes and Lie Groups}, author={Christoph Schweigert and Konrad Waldorf}, journal={arXiv: Differential Geometry}, year={2011}, pages={339-364} }

Compact Lie groups do not only carry the structure of a Riemannian manifold, but also canonical families of bundle gerbes. We discuss the construction of these bundle gerbes and their relation to loop groups. We present several algebraic structures for bundle gerbes with connection, such as Jandl structures, gerbe modules and gerbe bimodules, and indicate their applications to Wess–Zumino terms in two-dimensional field theories.

## 5 Citations

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…

String connections and Chern-Simons theory

- Mathematics, Computer Science
- 2009

A finite-dimensional and smooth formulation of string structures on spin bundles that enables it to prove that every string structure admits a string connection and that the possible choices form an affine space is presented.

Equivariant Holonomy for Bundles and Abelian Gerbes

- Mathematics
- 2012

This paper generalizes Bismut’s equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed differential form…

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…

A Higher Stacky Perspective on Chern–Simons Theory

- Physics
- 2015

The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern–Simons-type gauge field theories. We explain in some detail how…

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The Wess-Zumino term in two-dimensional conformal field theory is best understood as a surface holonomy of a bundle gerbe. We define additional structure for a bundle gerbe that allows to extend the…

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