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Gravitational Coset Models
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The algebra A(D-3)+++ dimensionally reduces to the E(D-1) symmetry algebra of (12-D)-dimensional supergravity. An infinite set of five-dimensional gravitational objects trivially embedded in D-dimensions is constructed by identifying the null geodesic motion on cosets embedded in the generalised Kac-Moody algebra A(D-3)+++. By analogy with supergravity these are bound states of dual gravitons. The metric interpolates continuously between exotic gravitational solutions generated by the action of the Geroch group but is not a continuously transforming solution of the Einstein-Hilbert action. We investigate mixed-symmetry fields in the brane sigma model, identify actions for the full interpolating bound state and understand the obstruction to the bound state being a solution of the Einstein-Hilbert action.
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From Tensor Algebras to Hyperbolic Kac-Moody Algebras
Simultaneous mutually commuting coset Virasoro actions are realized on the tensor algebra of the Feingold-Frenkel algebra, giving explicit decompositions and tensor ground states up to level five.
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