Constraints and the E10 coset model

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 ℓ ⩽ 3) 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 σ-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 × current) form in terms of the conserved E10 Noether current, and transform covariantly under an upper parabolic subgroup E+10 ⊂ E10. We discuss the possible implications of this result, and in particular exhibit a tantalizing link with the usual affine Sugawara construction in the truncation of E10 to its affine subgroup E9.