K(E10), Supergravity and Fermions

TL;DR

This paper explores the fermionic extension of the E10/K(E10) coset model, relating it to eleven-dimensional supergravity, and provides consistency checks and discrepancies that suggest further extensions are needed.

Contribution

It introduces a fermionic extension of the E10/K(E10) coset model, analyzes its algebraic structure, and compares it with supergravity, highlighting both agreements and discrepancies.

Findings

Agreement with supergravity at levels 0, 1, and 2

Identification of discrepancies at level 3

Indication for extending the model to infinite-dimensional fermionic representations

Abstract

We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E(10,R) are studied and the supergravity equations are rewritten using the resulting algebraic variables. The canonical bosonic and fermionic constraints are also analysed in this way, and the compatibility of supersymmetry with local K(E10) is investigated. We find that all structures involving A9 levels 0,1 and 2 nicely agree with expectations, and provide many non-trivial consistency checks of the existence of a supersymmetric extension of the E10/K(E10) coset model, as well as a new derivation of the `bosonic dictionary' between supergravity and coset variables. However, there are also definite discrepancies in some terms involving level 3, which suggest the need for an extension of the model to infinite-dimensional faithful representations of the fermionic degrees of freedom.