L-Algebra Models and Higher Chern-Simons Theories

Patricia Ritter, Christian Saemann

Research output: Contribution to journalArticle

6 Citations (Scopus)
41 Downloads (Pure)

Abstract

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
Volume28
Issue number9
DOIs
Publication statusPublished - 7 Oct 2016

Keywords

  • hep-th
  • math-ph
  • math.MP

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