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

TL;DR

This paper introduces a canonical construction of string 2-group models using a transgression-regression approach, linking gerbes, loop groups, and 2-group extensions in a novel way.

Contribution

It provides a choice-free, explicit construction of string 2-groups based on the basic gerbe and Mickelsson product, connecting gerbes with 2-group extensions.

Findings

Constructs string 2-groups from gerbes via transgression-regression.

Establishes a relation between multiplicative gerbes and 2-group extensions.

Utilizes recent work of Schommer-Pries to formalize the connection.

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.