L∞ Algebras for Extended Geometry from Borcherds Superalgebras
Artikel i vetenskaplig tidskrift, 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.

Författare

Martin Cederwall

Chalmers, Fysik, Teoretisk fysik

Institute of Theoretical Physics, Goteborg

Jakob Palmkvist

Institute of Theoretical Physics, Goteborg

Chalmers, Fysik, Teoretisk fysik

Communications in Mathematical Physics

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

Vol. 369 2 721-760

Bortom rum och tid

Vetenskapsrådet (VR), 2016-01-01 -- 2019-12-31.

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

Fundament

Grundläggande vetenskaper

DOI

10.1007/s00220-019-03451-2

Mer information

Senast uppdaterat

2019-07-16