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

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

Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems

We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the radius. In order to get those uniform rates of convergence the balls centres have to avoid a set whose size is estimated to be of similar order. This result can be applied to non-uniformly hyperbolic maps and to any invariant measure that satisfies a weak regularity condition. In particular it shows that the return times to balls is Poissonian for SRB measures on attractors.Comment: 28 page

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 $E_{10}$ in particular.Comment: 17 pages, 1 figure, LaTeX2e, amsfonts, amssymb, xspace, PiCTe

Canonical structure of the E10 model and supersymmetry

A coset model based on the hyperbolic Kac-Moody algebra E10 has been conjectured to underly eleven-dimensional supergravity and M theory. In this note we study the canonical structure of the bosonic model for finite- and infinite-dimensional groups. In the case of finite-dimensional groups like GL(n) we exhibit a convenient set of variables with Borel-type canonical brackets. The generalisation to the Kac-Moody case requires a proper treatment of the imaginary roots that remains elusive. As a second result, we show that the supersymmetry constraint of D=11 supergravity can be rewritten in a suggestive way using E10 algebra data. Combined with the canonical structure, this rewriting explains the previously observed association of the canonical constraints with null roots of E10. We also exhibit a basic incompatibility between local supersymmetry and the K(E10) `R symmetry', that can be traced back to the presence of imaginary roots and to the unfaithfulness of the spinor representations occurring in the present formulation of the E10 worldline model, and that may require a novel type of bosonisation/fermionisation for its resolution. This appears to be a key challenge for future progress with E10.Comment: 1+39 pages. v2: small corrections. Version to appear in PR

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

Pathogen avoidance by insect predators

Insects can detect cues related to the risk of attack by their natural enemies. Pathogens are among the natural enemies of insects and entomopathogenic fungi attack a wide array of host species. Evidence documents that social insects in particular have adapted behavioural mechanisms to avoid infection by fungal pathogens. These mechanisms are referred to as 'behavioural resistance'. However, there is little evidence for similar adaptations in non-social insects. We have conducted experiments to assess the potential of common insect predators to detect and avoid their entomopathogenic fungal natural enemy Beauveria bassiana. The predatory bug Anthocoris nemorum was able to detect and avoid nettle leaves that were treated with B. bassiana. Females laid fewer eggs on leaf halves contaminated with the pathogen. Similarly, females were very reluctant to contact nettle leaves contaminated with the fungus compared to uncontaminated control leaves in ‘no-choice’ experiments. Adult seven spot ladybirds, Coccinella septempunctata, overwinter in the litter layer often in groups. Adult C. septempunctata modified their overwintering behaviour in relation to the presence of B. bassiana conidia in soil and sporulating conspecifics by moving away from sources of infection. Furthermore active (non-overwintering) adult C. septempunctata were also able to detect and avoid B. bassiana conidia on different substrates; bean leaves, soil and sporulating on dead conspecifics. Our studies show that insect predators have evolved mechanisms to detect and avoid pathogens that they are susceptible to. Fungal pathogens may be significant mortality factors among populations of insect predators, especially long-lived species that must diapause before reproduction. Likewise, actively foraging species are more likely to come in contact with pathogens than predators that sit and wait for prey. These particular groups of insects will benefit from adaptations to avoid pathogens

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

Standard Model Fermions and N=8 supergravity

In a scheme originally proposed by M. Gell-Mann, and subsequently shown to be realized at the SU(3)xU(1) stationary point of maximal gauged SO(8) supergravity by N. Warner and one of the present authors, the 48 spin 1/2 fermions of the theory remaining after the removal of eight Goldstinos can be identified with the 48 quarks and leptons (including right-chiral neutrinos) of the Standard Model, provided one identifies the residual SU(3) with the diagonal subgroup of the color group SU(3)_c and a family symmetry SU(3)_f. However, there remained a systematic mismatch in the electric charges by a spurion charge of $\pm$1/6. We here identify the `missing' U(1) that rectifies this mismatch, and that takes a surprisingly simple, though unexpected form

Origin and growth of primordial black holes

In a previous paper we have argued that primordial black holes can arise from the formation and subsequent gravitational collapse of bound states of stable supermassive elementary particles (gravitinos) during the early radiation era. Here we offer a comprehensive picture, describing the evolution and growth of the resulting mini-black holes through both the radiation and matter dominated phases until the onset of inhomogeneities, by means of an exact metric solving Einstein's equations. We show that, thanks to a special enhancement effect producing an effective horizon above the actual event horizon, this process can explain the observed mass values of the earliest giant black holes