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 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.

34 pages

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Cited by in corpus (19)

• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• The Superspace of Geometrodynamics
• Supersymmetric quantum cosmological billiards
• Beyond E11
• The General Relativistic Two Body Problem and the Effective One Body Formalism
• A master exceptional field theory
• On supersymmetric E11 exceptional field theory
• On the E10/Massive Type IIA Supergravity Correspondence
• Fermionic Kac-Moody Billiards and Supergravity
• E10 and Gauged Maximal Supergravity
• U-gravity : $\mathbf{SL}(N)$
• Arithmetic and Hyperbolic Structures in String Theory
• Canonical structure of the E10 model and supersymmetry
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• Sugawara-type constraints in hyperbolic coset models
• The E10 Wheeler-DeWitt operator at low levels
• Bound States of String Theory and Beyond
• Automorphic correction of the hyperbolic Kac-Moody algebra $E_{10}$
• Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity