$E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies

Abstract

We define a generalized form of $L_{\infty }$-algebras called $E_2{L}_{\infty }$-algebras. As we show, these provide the natural algebraic framework for generalized geometry and the symmetries of double field theory as well as the gauge algebras arising in the tensor hierarchies of gauged supergravity. Our perspective shows that the kinematical data of the tensor hierarchy is an adjusted higher gauge theory, which is important for developing finite gauge transformations as well as non-local descriptions. Mathematically, $E_2{L}_{\infty }$-algebras shed some light on Loday's problem of integrating Leibniz algebras.

v2: 61 pages, restriction to E_2L_infty algebras, results added, presentation improved

References in corpus (29)

• Dualisation of Dualities, I
• Maximal gauged supergravity in three dimensions
• Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems
• Combinatorial operad actions on cochains
• The maximal D=7 supergravities
• On the perturbation lemma, and deformations
• Gauge Theories, Duality Relations and the Tensor Hierarchy
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Leibniz algebras, Lie racks, and digroups
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Tensor hierarchies, Borcherds algebras and E11
• Tensor hierarchies and Leibniz algebras
• The tensor hierarchy simplified
• Towards an M5-Brane Model I: A 6d Superconformal Field Theory
• Six-Dimensional (1,0) Superconformal Models and Higher Gauge Theory
• Algebra+Homotopy=Operad
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• Erratum to "Homological algebra of homotopy algebras"
• Electric/magnetic duality for chiral gauge theories with anomaly cancellation
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• Towards an M5-Brane Model II: Metric String Structures
• Symmetric homotopy theory for operads
• Adjusted Parallel Transport for Higher Gauge Theories
• Non-abelian Gerbes and Enhanced Leibniz Algebras
• The Non-Abelian Self-Dual String and the (2,0)-Theory
• Canonical gauges in higher gauge theory
• Generalized Higher Gauge Theory
• On the infinity category of homotopy Leibniz algebras