L∞ algebras and field theory
Abstract
We review and develop the general properties of $L_\infty$ algebras focusing on the gauge structure of the associated field theories. Motivated by the $L_\infty$ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the $L_\infty$ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an $L_\infty$ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full $L_\infty$ algebra for the interacting theory. The analysis suggests that $L_\infty$ algebras provide a classification of perturbative gauge invariant classical field theories.
- Publication:
-
Fortschritte der Physik
- Pub Date:
- March 2017
- DOI:
- 10.1002/prop.201700014
- arXiv:
- arXiv:1701.08824
- Bibcode:
- 2017ForPh..6500014H
- Keywords:
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- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 54 pages, v2: minor changes, refs. added, v3: minor corrections, version published in Fortsch.Phys