L∞ algebras and field theory

Hohm, Olaf; Zwiebach, Barton

doi:10.1002/prop.201700014

Title: L_∞ algebras and field theory

Journal Article · 19 March 2017 · Fortschritte der Physik

DOI: https://doi.org/10.1002/prop.201700014 · OSTI ID:1533219

Hohm, Olaf ^[1]; Zwiebach, Barton ^[2]

Stony Brook Univ., Stony Brook, NY (United States). Simons Center for Geometry and Physics; DOE/OSTI
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

In this paper, 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 theL_∞ 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.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0012567

OSTI ID:: 1533219

Journal Information:: Fortschritte der Physik, Journal Name: Fortschritte der Physik Journal Issue: 3-4 Vol. 65; ISSN 0015-8208

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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