2014/03/31 by Sylvain Lavau, Henning Samtleben, Thomas Strobl · 4 citations
Engineering · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Engineering #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Scroll #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.geomphys.2014.10.006
published as J.Geom.Phys. 86 (2014) 497-533 · 51 pages, 3 figures
openalex publication_date 2014/10/15 · arxiv created 2015/01/10 · arxiv updated 2015/01/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six spacetime dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show that the algebraic consistency constraints governing this system permit to define a Lie 3-algebra, generalizing the structural Lie algebra of a standard Yang-Mills theory to the setting of a higher bundle. Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type operator Q, this higher bundle can be compactly described by means of a Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to the Lie 3-algebra and its base the odd tangent bundle of spacetime equipped with the de Rham differential. The generalized Bianchi identities can then be retrieved concisely from Q2=0, which encode all the essence of the structural identities. Gauge transformations are identified as vertical inner automorphisms of such a bundle, their algebra being determined from a Q-derived bracket.