EL_\infty$-algebras, Generalized Geometry, and Tensor Hierarchies

We define a generalized form of $L_\infty$-algebras called $EL_\infty$-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 pe...

Full description

Saved in:
Bibliographic Details
Main Authors Borsten, Leron, Kim, Hyungrok, Saemann, Christian
Format Journal Article
LanguageEnglish
Published 31.05.2021
Subjects
Mathematics - Mathematical Physics
Physics - High Energy Physics - Theory
Physics - Mathematical Physics
Online AccessGet full text

Cover

More Information
Summary:We define a generalized form of $L_\infty$-algebras called $EL_\infty$-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, $EL_\infty$-algebras provide small resolutions of the operad $\mathcal{L}ie$, and they shed some light on Loday's problem of integrating Leibniz algebras.
Bibliography:EMPG-21-07
DOI:10.48550/arxiv.2106.00108