A Construction of String 2-Group Models using a Transgression-Regression Technique

Abstract

In this note we present a new construction of the string group that ends optionally in two different contexts: strict diffeological 2-groups or finite-dimensional Lie 2-groups. It is canonical in the sense that no choices are involved; all the data is written down and can be looked up (at least somewhere). The basis of our construction is the basic gerbe of Gawedzki-Reis and Meinrenken. The main new insight is that under a transgression-regression procedure, the basic gerbe picks up a multiplicative structure coming from the Mickelsson product over the loop group. The conclusion of the construction is a relation between multiplicative gerbes and 2-group extensions for which we use recent work of Schommer-Pries.

25 pages; v2 is the published version (with some minor corrections)

References in corpus (4)

• Higher-Dimensional Algebra V: 2-Groups
• Higher gauge theory I: 2-Bundles
• More Morphisms between Bundle Gerbes
• Polyakov-Wiegmann Formula and Multiplicative Gerbes

Cited by in corpus (12)

• Notes on generalized global symmetries in QFT
• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• Spin structures on loop spaces that characterize string manifolds
• String geometry vs. spin geometry on loop spaces
• Transgressive loop group extensions
• Higher geometry for non-geometric T-duals
• Principal $\infty$-Bundles and Smooth String Group Models
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Categorical Tori
• Chern correspondence for higher principal bundles
• Connes fusion of spinors on loop space
• Flat principal 2-group bundles and flat string structures