A Smooth Model for the String Group

Abstract

We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of Lie 2-groups. Moreover, we provide an explicit comparison of string structures for the two models and a uniqueness result for Lie 2-group models.

32 pages; v2: uniqueness result for 2-group models added (Th. 6.5), typo in title corrected; v3: construction of basic PU(H)-bundle discussed (Rem. 3.9), final version to appear in IMRN

References in corpus (3)

• Central Extensions of Smooth 2-Groups and a Finite-Dimensional String 2-Group
• Butterflies I: morphisms of 2-group stacks
• Lie Group Structures on Symmetry Groups of Principal Bundles

Cited by in corpus (9)

• Notes on generalized global symmetries in QFT
• The Lie group of bisections of a Lie groupoid
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• Infinitesimal 2-braidings and differential crossed modules
• Principal $\infty$-Bundles and Smooth String Group Models
• String structures associated to indefinite Lie groups
• Explicit Non-Abelian Gerbes with Connections
• Flat principal 2-group bundles and flat string structures