Constraints and the E10 Coset Model

TL;DR

This paper demonstrates that the constrained dynamics of a truncated E10 coset model precisely match the equations of motion of maximal supergravity, revealing a Sugawara-like structure in the constraints.

Contribution

It shows that supergravity constraints can be incorporated into the E10 coset model, establishing a covariant Sugawara-like formulation of the constraints.

Findings

Constrained E10 coset dynamics reproduce supergravity equations.

Bosonic constraints are expressible in a Sugawara-like form.

Constraints transform covariantly under E10+ subgroup.

Abstract

We continue the study of the one-dimensional E10 coset model (massless spinning particle motion on E10/K(E10) whose dynamics at low levels is known to coincide with the equations of motion of maximal supergravity theories in appropriate truncations. We show that the coset dynamics (truncated at levels less or equal to three) can be consistently restricted by requiring the vanishing of a set of constraints which are in one-to-one correspondence with the canonical constraints of supergravity. Hence, the resulting constrained sigma-model dynamics captures the full (constrained) supergravity dynamics in this truncation. Remarkably, the bosonic constraints are found to be expressible in a Sugawara-like (current x current) form in terms of the conserved E10 Noether current, and transform covariantly under an upper parabolic subgroup E10+ of E10. We discuss the possible implications of this result, and in particular exhibit a tantalising link with the usual affine Sugawara construction in the truncation of E10 to its affine subgroup E9.