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

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

Insect pathogenic fungi in biological control: status and future challenges

In Europe, insect pathogenic fungi have in decades played a significant role in biological control of insects. With respect to the different strategies of biological control and with respects to the different genera of insect pathogenic fungi, the success and potential vary, however. Classical biological control: no strong indication of potential. Inundation and inoculation biological control: success stories with the genera Metarhizium, Beauveria, Isaria/Paecilomyces and Lecanicillium (previously Verticillium). However, the genotypes employed seem to include a narrow spectrum of the many potentially useful genotypes. Conservation biological control: Pandora and Entomophthora have a strong potential, but also Beauveria has a potential to be explored further. The main bottleneck for further exploitation of insect pathogenic fungi in biological control is the limited knowledge of host pathogen interaction at the fungal genotype level

Physical States in d=3,N=2 Supergravity

To clarify some issues raised by D'Eath's recent proposal for the physical states of $N=1$ supergravity in four dimensions, we study pure (topological) $N=2$ supergravity in three dimensions, which is formally very similar, but much easier to solve. The wave functionals solving the quantum constraints can be understood in terms of arbitrary functions on the space of moduli and supermoduli, which is not Hausdorff. We discuss the implications for the wave functionals and show that these are not amenable to expansions in fermionic coordinates, but can serve as lowest-order solutions to the quantum constraints in an expansion in $\hbar$ in more realistic theories.Comment: 11 pages, Report DESY 93-125, THU-93/1

Monodromy Matrix in the PP-Wave Limit

We construct the monodromy matrix for a class of gauged WZWN models in the plane wave limit and discuss various properties of such systems.Comment: 16 page

Two-loop finiteness of D=2 supergravity

We establish two-loop (on shell) finiteness of certain supergravity theories in two dimensions. Possible implications of this result are discussedComment: 11 page

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

AdS3_3 vacua and RG flows in three dimensional gauged supergravities

We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times SO(4)})^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons gaugings $SO(4)\ltimes {\bf R}^6$ and $(SO(4)\ltimes {\bf R}^6)^2$, respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$ Yang-Mills theories coupled to supergravity. For the N=4 case, we study renormalization group flows between UV and IR $AdS_3$ vacua with the same amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an analytic solution whereas in another, with (2,0) supersymmetry, we give a numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e. they are driven by the expectation value of a relevant operator in the dual $SCFT_2$. These provide examples of v.e.v. flows between two $AdS_3$ vacua within a gauged supergravity framework.Comment: 35 pages in JHEP form, 3 figures, typos corrected, references adde