The gauge structure of generalised diffeomorphisms

TL;DR

This paper explores the gauge structure of generalized diffeomorphisms in M-theory, revealing an infinitely reducible gauge algebra with complex ghost structures and connections to tensor hierarchies and Borcherds algebras.

Contribution

It provides a covariant description of the gauge transformations, analyzes their infinite reducibility, and links the ghost structure to known algebraic sequences in M-theory.

Findings

The gauge algebra is infinitely reducible with an infinite tower of ghosts.

The ghost structure aligns with sequences in tensor hierarchies and Borcherds algebras.

The analysis confirms correct degrees of freedom counting using regularized sums.

Abstract

We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.