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 $4M L^{-1}$, where $L$ is the period and $M$ is the mass of the black hole. Outside the horizon, the solution is free of singularities and approaches the Schwarzschild solution as $L \rightarrow \infty$.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 2d2d σ\sigma-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 $A_1^{(1)}$ 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 ($=y$) and a variable one ($=t$). They hold for all $2d$ non-linear $\sigma$-models that are obtained by dimensional reduction of $G/H$ 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 $Y(e_8)$ 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