Generalised diffeomorphisms for E$_9$

TL;DR

This paper develops a new framework for generalized diffeomorphisms in E$_9$ exceptional field theory, extending the algebraic structure to infinite-dimensional Lie algebras and confirming its consistency with gauged supergravity.

Contribution

It introduces the first example of a generalized diffeomorphism algebra based on an infinite-dimensional Lie algebra, specifically E$_9$, and provides a generic expression for invariant tensors in extended geometry.

Findings

Transformations close when acting on fields

Reproduces gauged supergravity in two dimensions

Applicable to other affine algebras

Abstract

We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a generalised diffeomorphism algebra based on an infinite-dimensional Lie algebra and an infinite-dimensional coordinate module. As a byproduct, we give a simple generic expression for the invariant tensors used in any extended geometry. We perform a generalised Scherk--Schwarz reduction and verify that our transformations reproduce the structure of gauged supergravity in two dimensions. The results are valid also for other affine algebras.