L∞ algebras and field theory
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1701.08824.pdf
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444.72 KB
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9a177c34e752ab127262fabab11fec93
Author(s)
Hohm, Olaf
Zwiebach, Barton
Date Issued
March 2017
Journal
Fortschritte der Physik
Publisher
Wiley
Citation
Hohm, Olaf, and Barton Zwiebach. “L∞ Algebras and Field Theory.” Fortschritte Der Physik 65, no. 3–4 (March 2017): 1700014.
Version
Original manuscript
Abstract
We review and develop the general properties of L∞algebras focusing on the gauge structure of the associated field theories. Motivated by the L∞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∞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∞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∞algebra for the interacting theory. The analysis suggests that L∞algebras provide a classification of perturbative gauge invariant classical field theories.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1002/PROP.201700014
