Sugawara-type constraints in hyperbolic coset models

TL;DR

This paper develops an infinite-dimensional Sugawara-type construction for hyperbolic coset models, extending supergravity constraints into the E10 algebra, uniting different supergravity theories and offering insights into gravity's canonical constraints.

Contribution

It introduces an infinite set of constraints in the E10 algebra, extending previous finite truncations, and unites supergravity constraints within a single algebraic framework.

Findings

Extended constraints fill the past light-cone of the root lattice.

Construction uses E10 Weyl group and includes D=11 and D=10 IIB supergravity.

Potential implications for understanding open constraint algebras in gravity.

Abstract

In the conjectured correspondence between supergravity and geodesic models on infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the constraints play a central role. We present a Sugawara-type construction in terms of the E10 Noether charges that extends these constraints infinitely into the hyperbolic algebra, in contrast to the truncated expressions obtained in arXiv:0709.2691 that involved only finitely many generators. Our extended constraints are associated to an infinite set of roots which are all imaginary, and in fact fill the closed past light-cone of the Lorentzian root lattice. The construction makes crucial use of the E10 Weyl group and of the fact that the E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our extended constraints appear to unite in a remarkable manner the different canonical constraints of these two theories. This construction may also shed new light on the issue of `open constraint algebras' in traditional canonical approaches to gravity.