L∞ Algebras for Extended Geometry from Borcherds Superalgebras
Journal article, 2019

We examine the structure of gauge transformations in extended geometry, the framework unifying double geometry, exceptional geometry, etc. This is done by giving the variations of the ghosts in a Batalin–Vilkovisky framework, or equivalently, an L∞ algebra. The L∞ brackets are given as derived brackets constructed using an underlying Borcherds superalgebra B(gr+1) , which is a double extension of the structure algebra gr. The construction includes a set of “ancillary” ghosts. All brackets involving the infinite sequence of ghosts are given explicitly. All even brackets above the 2-brackets vanish, and the coefficients appearing in the brackets are given by Bernoulli numbers. The results are valid in the absence of ancillary transformations at ghost number 1. We present evidence that in order to go further, the underlying algebra should be the corresponding tensor hierarchy algebra.


Martin Cederwall

Institute of Theoretical Physics, Goteborg

Chalmers, Physics, Theoretical Physics

Jakob Palmkvist

Chalmers, Physics, Theoretical Physics

Institute of Theoretical Physics, Goteborg

Communications in Mathematical Physics

0010-3616 (ISSN) 1432-0916 (eISSN)

Vol. 369 2 721-760

Beyond space and time

Swedish Research Council (VR) (2015-4268), 2016-01-01 -- 2019-12-31.

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4/6/2022 1