$L_{\infty}$ Algebras and Field Theory - INSPIRE

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$L_{\infty}$ Algebras and Field Theory

Jan 30, 2017

54 pages

Published in:

Fortsch.Phys. 65 (2017) 3-4, 1700014

Published: Mar 1, 2017

e-Print:

1701.08824 [hep-th]

DOI:

10.1002/prop.201700014

Report number:

MIT-CTP-4875

View in:

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Abstract: (WILEY)

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.

Note:

54 pages, v2: minor changes, refs. added, v3: minor corrections, version published in Fortsch.Phys

field theory: perturbation theory
invariance: gauge
gauge field theory: nonabelian
Einstein
double field theory
field theory: interaction
field theory: string
algebra: Lie
Chern-Simons term
Yang-Mills

References(52)

Figures(0)

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