# Twisted Weil Algebras for the String Lie 2-Algebra

## TL;DR

This paper explores twisted Weil algebras associated with the string Lie 2-algebra, providing a framework for higher gauge theory connections and illustrating their application in constructing non-Abelian self-dual string solitons.

## Contribution

It introduces twisted Weil algebras for the string Lie 2-algebra and demonstrates their use in higher gauge theory and soliton construction.

## Key findings

- Derived twisted Weil algebras for the string Lie 2-algebra
- Connected algebraic structures to higher gauge theory
- Applied to construct non-Abelian self-dual string solitons

## Abstract

In this article, we give a concise summary of $L_\infty$-algebras viewed in terms of Chevalley-Eilenberg algebras, Weil algebras and invariant polynomials and their use in defining connections in higher gauge theory. Using this, we discuss the example of the string Lie 2-algebra in both the skeletal and the loop model. In both cases, we show how to arrive at the twisted Weil algebras which were used in arXiv:1705.02353 to construct a non-Abelian self-dual string soliton, see also arXiv:1712.06623, arXiv:0801.3480, arXiv:0910.4001.