L-Algebra Models and Higher Chern-Simons Theories

Patricia Ritter, Christian Saemann

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
160 Downloads (Pure)


We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In a first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of $L_\infty$-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In a second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie $p$-algebra extensions of $\mathfrak{so}(p+2)$. Finally, we study a number of $L_\infty$-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.
Original languageEnglish
Article number1650021
Number of pages46
JournalReviews in Mathematical Physics
Issue number9
Publication statusPublished - 7 Oct 2016


  • hep-th
  • math-ph
  • math.MP


Dive into the research topics of 'L-Algebra Models and Higher Chern-Simons Theories'. Together they form a unique fingerprint.

Cite this