Physical States at the Tachyonic Vacuum of Open String Field Theory

We illustrate a method for computing the number of physical states of open string theory at the stable tachyonic vacuum in level truncation approximation. The method is based on the analysis of the gauge-fixed open string field theory quadratic action that includes Fadeev-Popov ghost string fields. Computations up to level 9 in the scalar sector are consistent with Sen's conjecture about the absence of physical open string states at the tachyonic vacuum. We also derive a long exact cohomology sequence that relates relative and absolute cohomologies of the BRS operator at the non-perturbative vacuum. We use this exact result in conjunction with our numerical findings to conclude that the higher ghost number non-perturbative BRS cohomologies are non-empty.Comment: 43 pages, 16 eps figures, LaTe

The Spectrum of Open String Field Theory at the Stable Tachyonic Vacuum

We present a level (10,30) numerical computation of the spectrum of quadratic fluctuations of Open String Field Theory around the tachyonic vacuum, both in the scalar and in the vector sector. Our results are consistent with Sen's conjecture about gauge-triviality of the small excitations. The computation is sufficiently accurate to provide robust evidence for the absence of the photon from the open string spectrum. We also observe that ghost string field propagators develop double poles. We show that this requires non-empty BRST cohomologies at non-standard ghost numbers. We comment about the relations of our results with recent work on the same subject.Comment: 33 pages, 10 figure

COVID-19 Crisis: Shifting Educational Leadership Toward a New Normal - A Case Study

This study examines the lived experiences of educational leaders during the COVID-19 pandemic. Research has often pointed to the role of educational leadership and its relationship to the quality and well-being of a school’s culture and climate. Recently the coronavirus has created a crisis on a magnitude the world has never seen that has globally altered human interactions and created an educational new normal. Literature is quickly seeking to examine the impact on education, and while much of its effect is yet to be seen, this study advances the understanding of crisis leadership, distinct from crisis management, during the pandemic. The findings reveal leadership lessons connecting to paradoxes identified through the themes: communication, care, decision-making, trauma and stress, coping and well-being, growth, and new normal

Evolution of three Pyrenophora cereal pathogens: recent divergence, speciation and evolution of non-coding DNA

Three of the most important fungal pathogens of cereals are Pyrenophora tritici-repentis, the cause of tan spot on wheat, and Pyrenophora teres f. teres and Pyrenophora teres f. maculata, the cause of spot form and net form of net blotch on barley, respectively. Orthologous intergenic regions were used to examine the genetic relationships and divergence times between these pathogens. Mean divergence times were calculated at 519 kya (±30) between P. teres f. teres and P. teres f. maculata, while P. tritici-repentis diverged from both Pyrenophora teres forms 8.04 Mya (±138 ky). Individual intergenic regions showed a consistent pattern of co-divergence of the P. teres forms from P. tritici-repentis, with the pattern supported by phylogenetic analysis of conserved genes. Differences in calculated divergence times between individual intergenic regions suggested that they are not entirely under neutral selection, a phenomenon shared with higher Eukaryotes. P. tritici-repentis regions varied in divergence time approximately 5–12 Mya from the P. teres lineage, compared to the separation of wheat and barley some 12 Mya, while the P. teres f. teres and P. teres f. maculata intergenic region divergences correspond to the middle Pleistocene. The data suggest there is no correlation between the divergence of these pathogens the domestication of wheat and barley, and show P. teres f. teres and P. teres f. maculata are closely related but autonomous. The results are discussed in the context of speciation and the evolution of intergenic regions

Proof of vanishing cohomology at the tachyon vacuum

We prove Sen's third conjecture that there are no on-shell perturbative excitations of the tachyon vacuum in open bosonic string field theory. The proof relies on the existence of a special state A, which, when acted on by the BRST operator at the tachyon vacuum, gives the identity. While this state was found numerically in Feynman-Siegel gauge, here we give a simple analytic expression.Comment: 19 pages, 4 figures; v2: references adde

Female teat size is a reliable indicator of annual breeding success in European badgers: Genetic validation

Assessing which females have bred successfully is a central requirement in many ecological field studies, providing an estimate of the effective female population size. Researchers have applied teat measurements previously to assess whether females, in a variety of mammalian species, have bred; however, this technique has not been validated genetically. Furthermore, several analytical techniques are available to classify individuals, but their misclassification rates have not been compared. We used 22 microsatellite loci to assign maternity, with 95% confidence, within a high-density population of European badgers Meles meles, as plural and subterranean breeding means that maternity cannot be inferred from behavioural observations. The teat lengths and diameters of 136 females, measured May–July 1994–2005, from social groups in which all offspring were assigned a mother, were reliable indicators of recent breeding success. A Generalised Linear Mixed Model (GLMM) classified both breeding and non-breeding females with lower error rates than discriminant analyses and crude teat-size criteria. The GLMM model logit probability = −20 + 1.8 month + 1.6 mean teat length + 1.0 mean teat diameter can be applied quickly in the field to assess the probability with which a female badger should be assigned maternity. This is a low-cost measure which, after validation, could be used in other badger or mammalian populations to assess the breeding success of females. This may be a particularly useful welfare tool for veterinary practitioners, especially during badger culls

Identifying specific prefrontal neurons that contribute to autism-associated abnormalities in physiology and social behavior.

Functional imaging and gene expression studies both implicate the medial prefrontal cortex (mPFC), particularly deep-layer projection neurons, as a potential locus for autism pathology. Here, we explored how specific deep-layer prefrontal neurons contribute to abnormal physiology and behavior in mouse models of autism. First, we find that across three etiologically distinct models-in utero valproic acid (VPA) exposure, CNTNAP2 knockout and FMR1 knockout-layer 5 subcortically projecting (SC) neurons consistently exhibit reduced input resistance and action potential firing. To explore how altered SC neuron physiology might impact behavior, we took advantage of the fact that in deep layers of the mPFC, dopamine D2 receptors (D2Rs) are mainly expressed by SC neurons, and used D2-Cre mice to label D2R+ neurons for calcium imaging or optogenetics. We found that social exploration preferentially recruits mPFC D2R+ cells, but that this recruitment is attenuated in VPA-exposed mice. Stimulating mPFC D2R+ neurons disrupts normal social interaction. Conversely, inhibiting these cells enhances social behavior in VPA-exposed mice. Importantly, this effect was not reproduced by nonspecifically inhibiting mPFC neurons in VPA-exposed mice, or by inhibiting D2R+ neurons in wild-type mice. These findings suggest that multiple forms of autism may alter the physiology of specific deep-layer prefrontal neurons that project to subcortical targets. Furthermore, a highly overlapping population-prefrontal D2R+ neurons-plays an important role in both normal and abnormal social behavior, such that targeting these cells can elicit potentially therapeutic effects

Superstring field theory equivalence: Ramond sector

We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories that send solutions to solutions in a way that respects the linearized gauge symmetries in both sides and keeps the action of the solutions invariant. The perturbative spectrum around equivalent solutions is also isomorphic. The problem with the cubic theory implies that the correspondence of the linearized gauge symmetries cannot be extended to a correspondence of the finite gauge symmetries. Hence, our equivalence is only formal, since it relates a consistent theory to an inconsistent one. Nonetheless, we believe that the fact that the equivalence formally works suggests that a consistent modification of the cubic theory exists. We construct a theory that can be considered as a first step towards a consistent RNS cubic theory.Comment: v1: 24 pages. v2: 27 pages, significant modifications of the presentation, new section, typos corrected, references adde

Ghost story. II. The midpoint ghost vertex

We construct the ghost number 9 three strings vertex for OSFT in the natural normal ordering. We find two versions, one with a ghost insertion at z=i and a twist-conjugate one with insertion at z=-i. For this reason we call them midpoint vertices. We show that the relevant Neumann matrices commute among themselves and with the matrix $G$ representing the operator K1. We analyze the spectrum of the latter and find that beside a continuous spectrum there is a (so far ignored) discrete one. We are able to write spectral formulas for all the Neumann matrices involved and clarify the important role of the integration contour over the continuous spectrum. We then pass to examine the (ghost) wedge states. We compute the discrete and continuous eigenvalues of the corresponding Neumann matrices and show that they satisfy the appropriate recursion relations. Using these results we show that the formulas for our vertices correctly define the star product in that, starting from the data of two ghost number 0 wedge states, they allow us to reconstruct a ghost number 3 state which is the expected wedge state with the ghost insertion at the midpoint, according to the star recursion relation.Comment: 60 pages. v2: typos and minor improvements, ref added. To appear in JHE

Ghost story. III. Back to ghost number zero

After having defined a 3-strings midpoint-inserted vertex for the bc system, we analyze the relation between gh=0 states (wedge states) and gh=3 midpoint duals. We find explicit and regular relations connecting the two objects. In the case of wedge states this allows us to write down a spectral decomposition for the gh=0 Neumann matrices, despite the fact that they are not commuting with the matrix representation of K1. We thus trace back the origin of this noncommutativity to be a consequence of the imaginary poles of the wedge eigenvalues in the complex k-plane. With explicit reconstruction formulas at hand for both gh=0 and gh=3, we can finally show how the midpoint vertex avoids this intrinsic noncommutativity at gh=0, making everything as simple as the zero momentum matter sector.Comment: 40 pages. v2: typos and minor corrections, presentation improved in sect. 4.3, plots added in app. A.1, two refs added. To appear in JHE