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

Conformal and Quasiconformal Realizations of Exceptional Lie Groups

We present a nonlinear realization of E_8 on a space of 57 dimensions, which is quasiconformal in the sense that it leaves invariant a suitably defined ``light cone'' in 57 dimensions. This realization, which is related to the Freudenthal triple system associated with the unique exceptional Jordan algebra over the split octonions, contains previous conformal realizations of the lower rank exceptional Lie groups on generalized space times, and in particular a conformal realization of E_7 on a 27 dimensional vector space which we exhibit explicitly. Possible applications of our results to supergravity and M-Theory are briefly mentioned.Comment: 21 pages, 1 figure. Revised version. Connection between SU(8) and SL(8,R) bases clarified; formulas corrected; references adde

On the sigma-model structure of type IIA supergravity action in doubled field approach

In this letter we describe how to string together the doubled field approach by Cremmer, Julia, Lu and Pope with Pasti-Sorokin-Tonin technique to construct the sigma-model-like action for type IIA supergravity. The relation of the results with that of obtained in the context of searching for Superstring/M-theory hidden symmetry group is discussed.Comment: 9 pp, LATEX; published in JETP Let

Hidden Symmetries, Central Charges and All That

In this review we discuss hidden symmetries of toroidal compactifications of eleven-dimensional supergravity. We recall alternative versions of this theory which exhibit traces of the hidden symmetries when still retaining the massive Kaluza-Klein states. We reconsider them in the broader perspective of M-theory which incorporates a more extended variety of BPS states. We also argue for a new geometry that may underly these theories. All our arguments point towards an extension of the number of space-time coordinates beyond eleven.Comment: 19 pages (LATEX), contribution to the G\"ursey memorial Conference II, Istanbul, June 200

Maximal gauged supergravity in three dimensions

We construct maximally supersymmetric gauged N=16 supergravity in three dimensions, thereby obtaining an entirely new class of AdS supergravities. These models are not derivable from any known higher-dimensional theory, indicating the existence of a new type of supergravity beyond D=11. They are expected to be of special importance also for the conjectured AdS/CFT correspondence. One of their noteworthy features is a nonabelian generalization of the duality between scalar and vector fields in three dimensions. Among the possible gauge groups, SO(8)xSO(8) is distinguished as the maximal compact gauge group, but there are also more exotic possibilities such as F_4 x G_2.Comment: 10 pages, LaTeX2e, minor changes in text, references added, version to appear in Phys. Rev. Let

Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories

We analyze the symmetries that are realized on the massive Kaluza-Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza-Klein modes are massless. The latter admits an infinite-dimensional extension of the three-dimensional diffeomorphism group as local symmetry and, moreover, a current algebra associated to SL(D-2,R) together with the diffeomorphism algebra of the internal manifold as global symmetries. It is shown that the `broken phase' can be reconstructed by gauging a certain subgroup of the global symmetries. This deforms the three-dimensional diffeomorphisms to a gauged version, and it is shown that they can be governed by a Chern-Simons theory, which unifies the spin-2 modes with the Kaluza-Klein vectors. This provides a reformulation of D-dimensional Einstein gravity, in which the physical degrees of freedom are described by the scalars of a gauged non-linear sigma model based on SL(D-2,R)/SO(D-2), while the metric appears in a purely topological Chern-Simons form.Comment: 23 pages, minor changes, v3: published versio