TL;DR
This paper develops a comprehensive framework for extended geometry using Kac-Moody algebras, unifying various theories and providing a universal action formulation applicable to multiple cases.
Contribution
It introduces a general formulation of extended geometry with a unified approach to gauge transformations and dynamics, encompassing all known double and exceptional field theories.
Findings
Constructed generalized diffeomorphisms and solutions to the section constraint.
Identified conditions for the presence of ancillary gauge transformations.
Derived a universal (pseudo-)action applicable to multiple cases.
Abstract
We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. Generalised diffeomorphisms are constructed, as well as solutions to the section constraint. Generically, additional ("ancillary") gauge transformations are present, and we give a concrete criterion determining when they appear. A universal form of the (pseudo-)action determines the dynamics in all cases without ancillary transformations, and also for a restricted set of cases based on the adjoint representation of a finite-dimensional simple Lie group. Our construction reproduces (the internal sector of) all previously considered cases of double and exceptional field theories.
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