Lie 2-algebra models

TL;DR

This paper explores zero-dimensional field theories based on semistrict Lie 2-algebras, unifying models like IKKT and M-brane theories, and introduces solutions representing quantized 2-plectic manifolds including R^3, S^3, and Hpp-wave.

Contribution

It introduces a new class of Lie 2-algebra models that generalize existing matrix models and reveals their solutions as quantized manifolds, expanding the understanding of higher gauge theories.

Findings

Solutions as quantized 2-plectic manifolds

Quantizations of R^3, S^3, and Hpp-wave found

Higher BF-theory derived from Lie 2-algebra models

Abstract

In this paper, we begin the study of zero-dimensional field theories with fields taking values in a semistrict Lie 2-algebra. These theories contain the IKKT matrix model and various M-brane related models as special cases. They feature solutions that can be interpreted as quantized 2-plectic manifolds. In particular, we find solutions corresponding to quantizations of R^3, S^3 and a five-dimensional Hpp-wave. Moreover, by expanding a certain class of Lie 2-algebra models around the solution corresponding to quantized R^3, we obtain higher BF-theory on this quantized space.