algebras and field theory

2017/01/31 by Olaf Hohm, Barton Zwiebach · 161 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #BRST quantization #Black Holes and Theoretical Physics #Gauge theory #Introduction to gauge theory #Mathematical physics #Mathematics #Physics #Pure mathematics #String field theory #String theory #Supersymmetric gauge theory #Theoretical physics #hep-th #math-ph #math.MP

paper · pdf · doi:10.1002/prop.201700014

published in Fortschritte der Physik 65(3-4) (Wiley) · 54 pages, v2: minor changes, refs. added, v3: minor corrections, version published in Fortsch.Phys

openalex publication_date 2017/03/01 · arxiv created 2017/03/26 · openalex created_date 2017/04/07 · arxiv updated 2017/04/26 · openalex updated_date 2026/08/05

Abstract

We review and develop the general properties of algebras focusing on the gauge structure of the associated field theories. Motivated by the 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 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 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 algebra for the interacting theory. The analysis suggests that algebras provide a classification of perturbative gauge invariant classical field theories.

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