An exceptional geometry for d=11 supergravity?

We analyze the algebraic constraints of the generalized vielbein in SO(1,2) x SO(16) invariant d=11 supergravity, and show that the bosonic degrees of freedom of d=11 supergravity, which become the physical ones upon reduction to d=3, can be assembled into an E_8-valued vielbein already in eleven dimensions. A crucial role in the construction is played by the maximal nilpotent commuting subalgebra of E_8, of dimension 36, suggesting a partial unification of general coordinate and tensor gauge transformations.Comment: 16 pages, LaTeX2

On the Yangian Y(e_8) quantum symmetry of maximal supergravity in two dimensions

We present the algebraic framework for the quantization of the classical bosonic charge algebra of maximally extended (N=16) supergravity in two dimensions, thereby taking the first steps towards an exact quantization of this model. At the core of our construction is the Yangian algebra $Y(e_8)$ whose RTT presentation we discuss in detail. The full symmetry algebra is a centrally extended twisted version of the Yangian double $DY(e_8)_c$. We show that there exists only one special value of the central charge for which the quantum algebra admits an ideal by which the algebra can be divided so as to consistently reproduce the classical coset structure $E_{8(8)}/SO(16)$ in the limit $\hbar\to 0$.Comment: 21 pages, LaTeX2

The Minimal Unitary Representation of E_8(8)

We give a new construction of the minimal unitary representation of the exceptional group E_8(8) on a Hilbert space of complex functions in 29 variables. Due to their manifest covariance with respect to the E_7(7) subgroup of E_8(8) our formulas are simpler than previous realizations, and thus well suited for applications in superstring and M theory.Comment: 24 pages, 1 figure, version to be published in ATM

The Sugawara generators at arbitrary level

We construct an explicit representation of the Sugawara generators for arbitrary level in terms of the homogeneous Heisenberg subalgebra, which generalizes the well-known expression at level 1. This is achieved by employing a physical vertex operator realization of the affine algebra at arbitrary level, in contrast to the Frenkel--Kac--Segal construction which uses unphysical oscillators and is restricted to level 1. At higher level, the new operators are transcendental functions of DDF ``oscillators'' unlike the quadratic expressions for the level-1 generators. An essential new feature of our construction is the appearance, beyond level 1, of new types of poles in the operator product expansions in addition to the ones at coincident points, which entail (controllable) non-localities in our formulas. We demonstrate the utility of the new formalism by explicitly working out some higher-level examples. Our results have important implications for the problem of constructing explicit representations for higher-level root spaces of hyperbolic Kac--Moody algebras, and $E_{10}$ in particular.Comment: 17 pages, 1 figure, LaTeX2e, amsfonts, amssymb, xspace, PiCTe

Godiva

In lieu of an abstract, below is the essay\u27s first paragraph. You\u27re really going out like that? I said. Why not? She said. You could catch cold like that

Shalott

In lieu of an abstract, below is the essay\u27s first paragraph. Singing a song of darlings locked upon the castle door, and fenny things and summer leaves, and the raven\u27s quote \u27Nevermore\u27