Generalised geometry, eleven dimensions and E11

We construct the non-linear realisation of E11 and its first fundamental representation in eleven dimensions at low levels. The fields depend on the usual coordinates of space-time as well as two form and five form coordinates. We derive the terms in the dynamics that contain the three form and six form fields and show that when we restricted their field dependence to be only on the usual space-time we recover the correct self-duality relation. Should this result generalise to the gravity fields then the non-linear realisation is an extension of the maximal supergravity theory, as previously conjectured. We also comment on the connections between the different approaches to generalised geometry.Comment: 17 pages, Trivial typos corrected in version one and a substantial note added which gives the equation of motion relating the gravity field to its dua

IIA/IIB Supergravity and Ten-forms

We perform a careful investigation of which p-form fields can be introduced consistently with the supersymmetry algebra of IIA and/or IIB ten-dimensional supergravity. In particular the ten-forms, also known as "top-forms", require a careful analysis since in this case, as we will show, closure of the supersymmetry algebra at the linear level does not imply closure at the non-linear level. Consequently, some of the (IIA and IIB) ten-form potentials introduced in earlier work of some of us are discarded. At the same time we show that new ten-form potentials, consistent with the full non-linear supersymmetry algebra can be introduced. We give a superspace explanation of our work. All of our results are precisely in line with the predictions of the E(11) algebra.Comment: 17 page

Goldstinos, Supercurrents and Metastable SUSY Breaking in N=2 Supersymmetric Gauge Theories

We construct an N=2 supersymmetric generalization of the N=1 supercurrent formalism of Komargodski and Seiberg (KS) and use it to show that N=2 theories with linear superconformal anomalies cannot break SUSY under certain broad assumptions. This result suggests that there are no metastable SUSY breaking vacua in a large class of theories that includes N=2 Super Yang-Mills (SYM).Comment: 19 pages; minor revisions; JHEP versio

Maximal supergravity in D=10: forms, Borcherds algebras and superspace cohomology

We give a very simple derivation of the forms of $N=2,D=10$ supergravity from supersymmetry and SL(2,\bbR) (for IIB). Using superspace cohomology we show that, if the Bianchi identities for the physical fields are satisfied, the (consistent) Bianchi identities for all of the higher-rank forms must be identically satisfied, and that there are no possible gauge-trivial Bianchi identities ($dF=0$) except for exact eleven-forms. We also show that the degrees of the forms can be extended beyond the spacetime limit, and that the representations they fall into agree with those predicted from Borcherds algebras. In IIA there are even-rank RR forms, including a non-zero twelve-form, while in IIB there are non-trivial Bianchi identities for thirteen-forms even though these forms are identically zero in supergravity. It is speculated that these higher-rank forms could be non-zero when higher-order string corrections are included.Comment: 15 pages. Published version. Some clarification of the tex

Higher derivative type II string effective actions, automorphic forms and E11

By dimensionally reducing the ten-dimensional higher derivative type IIA string theory effective action we place constraints on the automorphic forms that appear in the effective action in lower dimensions. We propose a number of properties of such automorphic forms and consider the prospects that E11 can play a role in the formulation of the higher derivative string theory effective action.Comment: 34 page

Visual Acuity Loss and Associated Risk Factors in the Retrospective Progression of Stargardt Disease Study (ProgStar Report No. 2)

PURPOSE: To examine the association between characteristics of Stargardt disease and visual acuity (VA), to estimate the longitudinal rate of VA loss, and to identify risk factors for VA loss. DESIGN: Retrospective, multicenter cohort study. PARTICIPANTS: A total of 176 patients (332 eyes) with molecularly and clinically confirmed Stargardt disease enrolled from the United States and Europe. METHODS: Standardized data report forms were used to collect retrospective data on participants' characteristics and best-corrected or presenting VA from medical charts. Linear models with generalized estimating equations were used to estimate the cross-sectional associations, and linear mixed effects models were used to estimate the longitudinal VA loss. MAIN OUTCOME MEASURES: Yearly change in VA. RESULTS: The median duration of observation was 3.6 years. At baseline, older age of symptom onset was associated with better VA, and a longer duration of symptoms was associated with worse VA. Longitudinal analysis estimated an average of 0.3 lines loss (P 30 years showed 0.4 lines slower change of VA per year (P = 0.01) compared with patients with onset age ≤14 years. CONCLUSIONS: Given the overall slow rate of VA loss, VA is unlikely to be a sensitive outcome measure for treatment trials of Stargardt disease. However, given the faster decline in younger patients and those with no or mild visual impairment, VA may be a potential outcome measure for trials targeting such subgroups of patients. These observations will need to be assessed in a prospective study bearing in mind the inherent limitations of retrospective datasets

Constraints on Automorphic Forms of Higher Derivative Terms from Compactification

By dimensionally reducing the higher derivative corrections of ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1} automorphic forms that occur in d=10-n dimensions. In particular we argue that these automorphic forms involve the representation of E_{n+1} with fundamental weight \lambda^{n+1}, which is also the representation to which the string charges in d dimensions belong. We also consider a similar calculation for the reduction of higher derivative terms in eleven-dimensional M-theory.Comment: Minor corrections, to appear in JHE

Growth dynamics and the evolution of cooperation in microbial populations

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.Comment: 26 pages, 6 figure

Till death (or an intruder) do us part: intrasexual-competition in a monogamous Primate

Polygynous animals are often highly dimorphic, and show large sex-differences in the degree of intra-sexual competition and aggression, which is associated with biased operational sex ratios (OSR). For socially monogamous, sexually monomorphic species, this relationship is less clear. Among mammals, pair-living has sometimes been assumed to imply equal OSR and low frequency, low intensity intra-sexual competition; even when high rates of intra-sexual competition and selection, in both sexes, have been theoretically predicted and described for various taxa. Owl monkeys are one of a few socially monogamous primates. Using long-term demographic and morphological data from 18 groups, we show that male and female owl monkeys experience intense intra-sexual competition and aggression from solitary floaters. Pair-mates are regularly replaced by intruding floaters (27 female and 23 male replacements in 149 group-years), with negative effects on the reproductive success of both partners. Individuals with only one partner during their life produced 25% more offspring per decade of tenure than those with two or more partners. The termination of the pair-bond is initiated by the floater, and sometimes has fatal consequences for the expelled adult. The existence of floaters and the sporadic, but intense aggression between them and residents suggest that it can be misleading to assume an equal OSR in socially monogamous species based solely on group composition. Instead, we suggest that sexual selection models must assume not equal, but flexible, context-specific, OSR in monogamous species.Wenner-Gren Foundation, L.S.B. Leakey Foundation, the National Geographic Society, National Science Foundation (BCS- 0621020), the University of Pennsylvania Research Foundation and the Zoological Society of San Diego, German Science Foundation (HU 1746-2/1