795 research outputs found
Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions
We present the maximally supersymmetric three-dimensional gauged
supergravities. Owing to the special properties of three dimensions --
especially the on-shell duality between vector and scalar fields, and the
purely topological character of (super)gravity -- they exhibit an even richer
structure than the gauged supergravities in higher dimensions. The allowed
gauge groups are subgroups of the global E_8 symmetry of ungauged N=16
supergravity. They include the regular series SO(p,8-p) x SO(p,8-p) for all
p=0,1,...,4, the group E_8 itself, as well as various noncompact forms of the
exceptional groups E_7, E_6 and F_4 x G_2. We show that all these theories
admit maximally supersymmetric ground states, and determine their background
isometries, which are superextensions of the anti-de Sitter group SO(2,2). The
very existence of these theories is argued to point to a new supergravity
beyond the standard D=11 supergravity.Comment: 41 pages, LaTeX2e, minor changes, references adde
Yangian Symmetry in Integrable Quantum Gravity
Dimensional reduction of various gravity and supergravity models leads to
effectively two-dimensional field theories described by gravity coupled G/H
coset space sigma-models. The transition matrices of the associated linear
system provide a complete set of conserved charges. Their Poisson algebra is a
semi-classical Yangian double modified by a twist which is a remnant of the
underlying coset structure. The classical Geroch group is generated by the
Lie-Poisson action of these charges. Canonical quantization of the structure
leads to a twisted Yangian double with fixed central extension at a critical
level.Comment: 23 pages, 1 figure, 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
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of
dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space
sigma-models coupled to gravity and a dilaton. Using methods developed in the
context of flat space integrable systems, the Wheeler-DeWitt equations for
these models can be reduced to a modified version of the Knizhnik-Zamolodchikov
equations from conformal field theory, the insertions given by singularities in
the spectral parameter plane. This basic result in principle permits the
explicit construction of solutions, i.e. physical states of the quantized
theory. In this way, we arrive at integrable models of quantum gravity with
infinitely many self-interacting propagating degrees of freedom.Comment: 41 pages, 2 figures, Lectures given at NATO Advanced Study Institute
on Quantum Fields and Quantum Space Time, Cargese, France, 22 July - 3 Augus
Gauged Supergravities in Three Dimensions: A Panoramic Overview
Maximal and non-maximal supergravities in three spacetime dimensions allow
for a large variety of semisimple and non-semisimple gauge groups, as well as
complex gauge groups that have no analog in higher dimensions. In this
contribution we review the recent progress in constructing these theories and
discuss some of their possible applications.Comment: 32 pages, 1 figure, Proceedings of the 27th Johns Hopkins workshop:
Goteborg, August 2003; references adde
On the quantization of isomonodromic deformations on the torus
The quantization of isomonodromic deformation of a meromorphic connection on
the torus is shown to lead directly to the Knizhnik-Zamolodchikov-Bernard
equations in the same way as the problem on the sphere leads to the system of
Knizhnik-Zamolodchikov equations. The Poisson bracket required for a
Hamiltonian formulation of isomonodromic deformations is naturally induced by
the Poisson structure of Chern-Simons theory in a holomorphic gauge fixing.
This turns out to be the origin of the appearance of twisted quantities on the
torus.Comment: 13 pages, LaTex2
Consistent Pauli reduction on group manifolds
We prove an old conjecture by Duff, Nilsson, Pope and Warner asserting that
the NS-NS sector of supergravity (and more general the bosonic string) allows
for a consistent Pauli reduction on any d-dimensional group manifold G, keeping
the full set of gauge bosons of the G x G isometry group of the bi-invariant
metric on G. The main tool of the construction is a particular generalised
Scherk-Schwarz reduction ansatz in double field theory which we explicitly
construct in terms of the group's Killing vectors. Examples include the
consistent reduction from ten dimensions on and on similar
product spaces. The construction is another example of globally geometric
non-toroidal compactifications inducing non-geometric fluxes.Comment: 16 page
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