3,182 research outputs found
Extensions of supersymmetric spin systems
A discussion of supersymmetric spin systems is presented extending the results obtained in a recent paper (see ibid., vol.9, p.1497 (1976)). A two-dimensional model is given and gauge invariance is defined; the latter is shown to necessitate the introduction of further spin operators
Gravitational Billiards, Dualities and Hidden Symmetries
The purpose of this article is to highlight the fascinating, but only very
incompletely understood relation between Einstein's theory and its
generalizations on the one hand, and the theory of indefinite, and in
particular hyperbolic, Kac Moody algebras on the other. The elucidation of this
link could lead to yet another revolution in our understanding of Einstein's
theory and attempts to quantize it.Comment: 37 pages, invited contribution to the volume "100 years of relativity
spacetime structure: Einstein and beyond", ed. A. Ashteka
Mathematics - A beauty and a beast
The mapping of the largest exceptional Lie group, E8, is a milestone for enthusiasts for the aesthetics of mathematics. But this embodiment of complex symmetry could be of interest to fundamental physics, too
On Hidden Symmetries in d=11 Supergravity and Beyond
Invited talk at the conference "Fundamental Interactions: From Symmetries to
Black Holes" in honor of Francois Englert, 24 - 27 March, Universite Libre de
Bruxelles, BelgiumComment: 14 page
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
A Periodic Analog of the Schwarzschild Solution
We construct a new exact solution of Einstein's equations in vacuo in terms
of Weyl canonical coordinates. This solution may be interpreted as a black hole
in a space-time which is periodic in one direction and which behaves
asymptotically like the Kasner solution with Kasner index equal to ,
where is the period and is the mass of the black hole. Outside the
horizon, the solution is free of singularities and approaches the Schwarzschild
solution as .Comment: 6 pages, preprint DESY-TH 94-03
Relativistic minimal surfaces
We find classical solutions to the equations of motion of an M-dimensional surface moving in a higher-dimensional embedding space-time for arbitrary M. In the case of closed membranes, solutions exist for any topological type (genus)
Conformal internal symmetry of -models coupled to gravity and a dilaton
General Relativity reduced to two dimensions possesses a large group of
symmetries that exchange classical solutions. The associated Lie algebra is
known to contain the affine Kac-Moody algebra and half of a real
Witt algebra. In this paper we exhibit the full symmetry under the semi-direct
product of \Lie{A_1^{(1)}} by the Witt algebra \Lie{\Wir}. Furthermore we
exhibit the corresponding hidden gauge symmetries. We show that the theory can
be understood in terms of an infinite dimensional potential space involving all
degrees of freedom: the dilaton as well as matter and gravitation. In the
dilaton sector the linear system that extends the previously known Lax pair has
the form of a twisted self-duality constraint that is the analog of the
self-duality constraint arising in extended supergravities in higher spacetime
dimensions. Our results furnish a group theoretical explanation for the
simultaneous occurrence of two spectral parameters, a constant one () and a
variable one (). They hold for all non-linear -models that are
obtained by dimensional reduction of models in three dimensions coupled
to pure gravity. In that case the Lie algebra is \Lie{\Wir \semi G^{(1)}};
this symmetry acts on a set of off shell fields (in a fixed gauge) and
preserves the equations of motion.Comment: 44 pages, LATE
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
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