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.

47 pages, presentation improved, version published in JHEP

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Cited by in corpus (10)

• Towards an M5-Brane Model I: A 6d Superconformal Field Theory
• 4-d semistrict higher Chern-Simons theory I
• Lie n-algebras of BPS charges
• $L_{\infty }$-Algebra Models and Higher Chern-Simons Theories
• A Lie based 4-dimensional higher Chern-Simons theory
• Algebraic formulation of higher gauge theory
• Automorphisms of Strong Homotopy Lie Algebras of Local Observables
• Higher Affine Connections
• Strongly Homotopy Lie Algebras from Multisymplectic Geometry
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