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$L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism

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arxiv 1809.09899 v4 pith:L3FVI7GL submitted 2018-09-26 hep-th math-phmath.MP

Branislav Jurco , Lorenzo Raspollini , Christian Saemann , Martin Wolf This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords fieldtheoriesclassicalinftyalgebrasbatalin-vilkoviskydetailformalism
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abstract

We review in detail the Batalin-Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. In particular, we show how a field theory gives rise to an $L_\infty$-algebra and how quasi-isomorphisms between $L_\infty$-algebras correspond to classical equivalences of field theories. A few experts may be familiar with parts of our discussion, however, the material is presented from the perspective of a very general notion of a gauge theory. We also make a number of new observations and present some new results. Most importantly, we discuss in great detail higher (categorified) Chern-Simons theories and give some useful shortcuts in usually rather involved computations.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The BEF Symplectic Form: A Lagrangian Perspective

    hep-th 2026-04 unverdicted novelty 7.0 of 10

    The BEF symplectic form is derived from L∞-Lagrangians via covariant phase space methods and coincides with the Barnich-Brandt form for second-order equations of motion.

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    The authors introduce half-adjusted higher Chern-Simons theories, obtained by a cotangent completion of adjusted L8-algebras, which admit consistent gauge transformations and equations of motion implying full flatness.

  3. Covariant phase space and $L_\infty$ algebras

    hep-th 2025-06 conditional novelty 7.0 of 10

    A covariant phase space symplectic form is constructed for any L∞ Lagrangian field theory using a 'sigmoid' operator, and is verified in scalar, Yang-Mills, general relativity, and p-adic string examples.

  4. Sandwich Construction of Symmetry TFTs for the Centre Symmetries of Chern-Simons, Yang-Mills, and Einstein Gravity

    hep-th 2025-09 conditional novelty 5.0 of 10

    Constructs AKSZ sandwich SymTFTs with stacky target spaces that encode the center symmetries of Chern-Simons, Yang-Mills, and MacDowell-Mansouri gravity.

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