Work

L∞-algebra models and higher Chern–Simons theories

Year: 2016

Type: article

Abstract: We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the 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 [Formula: see text]-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the 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 [Formula: see text]-algebra extensions of [Formula: see text]. Finally, we study a number of [Formula: see text]-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.

Source: Reviews in Mathematical Physics

DOI: 10.1142/s0129055x16500215

Authors: Patricia Ritter, Christian Sämann

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, University of Bologna, Heriot-Watt University, Maxwell Institute for Mathematical Sciences

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Science and Technology Facilities Council

Awards: G163389775, G3367350104, Particle Theory at the Higgs Centre