1,866 research outputs found
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
whose RTT presentation we discuss in detail. The full symmetry algebra is a
centrally extended twisted version of the Yangian double . 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 in the
limit .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 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
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