425 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
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
- …