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The induced two-dimensional topological N=1 supersymmetric sigma model on a differential Poisson manifold M presented in arXiv:1503.05625 is shown to be a special case of the induced Poisson sigma model on the bi-graded supermanifold T[0,1]M. The bi-degree comprises the standard N-valued target space degree, corresponding to the form degree on the worldsheet, and an additional Z-valued fermion number, corresponding to the degree in the differential graded algebra of forms on M. The N=1 supersymmetry stems from the compatibility between the (extended) differential Poisson bracket and the de Rham differential on M. The latter is mapped to a nilpotent vector field Q of bi-degree (0,1) on T*[1,0](T[0,1]M), and the covariant Hamiltonian action is Q-exact. New extended supersymmetries arise as inner derivatives along special bosonic Killing vectors on M that induce Killing supervector fields of bi-degree (0,-1) on T*[1,0](T[0,1]M)., Comment: 39 pages

Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as to zero-form constraints on-shell. Two examples thereof are a twisting of C[(Z_2)^3] that yields the original model, and the Clifford algebra Cl_2n which provides an FCS formulation of the bosonic Konstein--Vasiliev model with gauge algebra hu(4^{n-1},0)., Comment: 44 pages

We review various off-shell formulations for interacting higher-spin systems in dimensions 3 and 4. Associated with higher-spin systems in spacetime dimension 4 is a Chern-Simons action for a superconnection taking its values in a direct product of an infinite-dimensional algebra of oscillators and a Frobenius algebra. A crucial ingredient of the model is that it elevates the rigid closed and central two-form of Vasiliev's theory to a dynamical 2-form and doubles the higher-spin algebra, thereby considerably reducing the number of possible higher spin invariants and giving a nonzero effective functional on-shell. The two action principles we give for higher-spin systems in 3D are based on Chern-Simons and BF models. In the first case, the theory we give unifies higher-spin gauge fields with fractional-spin fields and an internal sector. In particular, Newton's constant is related to the coupling constant of the internal sector. In the second case, the BF action we review gives the fully nonlinear Prokushkin-Vasiliev, bosonic equations for matter-coupled higher spins in 3D. We present the truncation to a single, real matter field relevant in the Gaberdiel-Gopakumar holographic duality. The link between the various actions we present is the fact that they all borrow ingredients from Topological Field Theory. It has bee conjectured that there is an underlying and unifying 2-dimensional first-quantised description of the previous higher-spin models in 3D and 4D, in the form of a Cattaneo-Felder-like topological action containing fermionic fields., Comment: 41+1 pages. References added and reorganized, corrected typos, last paragraph of section 2 re-written. Contribution to the proceedings of the International Workshop on Higher Spin Gauge Theories (4-6 November 2015, Singapore)

The Lema\'itre-Toman-Bondi (LTB) models have reported to suffer from incompatibility with cosmological observations and fine-tuning of the observer's location. Further analysis of these issues indicates that they could be resolved by models that are compatible with the supernova Ia data, but less inhomogeneous than those that have been presented in the literature so far. We study if such models exist by employing the degrees of freedom of the LTB models in a novel manner. We discovered two scenarios which may meet the expectations, but extensive numerical and analytical investigation showed them inviable. We extended our studies to the $\Lambda$LTB models, which generalizes the LTB models by including a non-zero cosmological constant $\Lambda$ in Einsteins equations. This adds an additional degree of freedom for the earlier scenarios and introduces a new scenario capable of meeting the expectations. However, extensive numerical and analytical investigation reveals that inclusion of $\Lambda$ does not enhance the viability of the models. We identify the lack of degrees of freedom to be the reason for the unviability. However, the method presented here can be generalized to models including more degrees of freedom, like the Szekeres models, which have more promise to overcome the issues in the LTB models., Comment: 15 pages including 1 appendix and 4 figures

This study was designed to investigate the relationship between participation in federally mandated college and career-preparatory programs--known as programs of study (POS)--and high school achievement outcomes. POS are an organized approach to college and career readiness that offer an aligned sequence of courses spanning secondary and postsecondary education, blending standards-based academic and technical content, allowing students to earn postsecondary credit while in high school, and leading to an industry-recognized credential or certificate at the postsecondary level or an associate or baccalaureate degree. The sample includes 6,638 students from three urban districts in three different states. This study employed a multi-method, longitudinal, quasi-experimental design. Qualitative measures included adherence to the legislatively mandated components of POS. In the quantitative portion of the study, we employed two different statistical approaches to the data in each district. First, we estimated the effects of enrolling in POS and the number of career and technical education (CTE) credits earned on GPA and graduation using an instrumental variable approach. In addition, we also addressed specific policy questions about completing a POS compared to other high school trajectories through posthoc multiple regression analyses. The outcomes show that in the first district, enrollment in POS schools caused more students to graduate by increasing the number of CTE credits they earned. In all three districts, earning more CTE credits was associated with graduation, although the results for the other two districts did not support the type of causal inferences we were able to draw from the first district's outcomes. We also found that POS students earned significantly more STEM or AP credits than comparison students, depending on the implementation context. POS students outperformed other students on technical measures at little to no cost to overall academic achievement. Across all districts, participation in programs associated with accruing college credits in high school (e.g., dual enrollment) was low, as was the incidence of earning an industry-recognized credential, two key elements of POS. We lacked the research funding to examine whether POS led to postsecondary degrees; however, senior exit survey results indicated that similar numbers of intervention and comparison students planned to attend a four-year college full time. This suggests that POS can be offered to high school students with no harm to their college aspirations or preparation. In addition, significantly more POS students indicated that their college studies would be related to their high school program, suggesting that students who enroll in a POS often continue their education in the same program area, and reap the benefits of having begun that preparation while still in high school. Our primary recommendation is for districts to seek ways to increase the number of CTE credits earned by high school students, because in all three districts, earning more CTE credits was associated with graduation. Other recommendations include re-examining dual enrollment programs so that more students participate, encouraging more people from industry backgrounds to become high school teachers, and improving data collection so that the efficacy of interventions may be better evaluated. All of these recommendations should improve POS, secondary school outcomes, and preparation of our nation's youth for postsecondary education and careers. The following are appended: (1) Quantitative Technical Appendix; (2) Qualitative Technical Appendix; (3) Classroom Observation Form; and (4) Senior Exit Survey Respondent Characteristics.

We propose a covariant Hamiltonian action for the Prokushkin and Vasiliev's matter coupled higher spin gravity in three dimensions. The action is formulated on ${\cal X}_4 \times {\cal Z}_2$ where ${\cal X}_4$ is an open manifold whose boundary contains spacetime and ${\cal Z}_2$ is a noncommutative twistor space. We examine various consistent truncations to models of BF type in ${\cal X}_4$ and ${\cal Z}_2$ with B$^2$ terms and central elements. They are obtained by integrating out the matter fields in the presence of a vacuum expectation value $\nu\in \mathbb{R}$ for the zero-form master field. For $\nu=0$, we obtain a model on ${\cal X}_4$ containing Blencowe's action and a model on ${\cal Z}_2$ containing the Prokushkin--Segal--Vasiliev action. For generic $\nu$ (including $\nu=0$), we propose an alternative model on ${\cal X}_4$ with gauge fields in the Weyl algebra of Wigner's deformed oscillator algebra and Lagrange multipliers in the algebra of operators acting in the Fock representation space of the deformed oscillators., Comment: 33 + 1 pages, no figure. Minor typos corrected

The dynamics of the tilted axisymmetric Bianchi IX cosmological models are explored allowing energy flux in the source fluid. The Einstein equations and the continuity equation are presented treating the equation of state $w$ and the tilt angle of the fluid $\lambda$ as time dependent functions, but when analysing the phase space $w$ and $\lambda$ are considered free parameters and the shear, the vorticity and the curvature of the spacetime span a three-dimensional phase space that contains seven fixed points. One of them is an attractor that inflates the universe anisotropically, thus providing a counter example to the cosmic no-hair conjecture. Also, examples of a realistic though fine-tuned cosmologies are presented wherein the rotation can grow significant towards the present epoch but the shear stays within the observational bounds. The examples suggest that the model used here can explain the parity-violating anomalies of the cosmic microwave background. The result significantly differs from an earlier study, where a non-axisymmetric Bianchi IX type with a tilted perfect dust source was found to induce too much shear for observationally significant vorticity., Comment: Accepted in PRD. 18 pages including appendices, 15 figures

We provide an off-shell formulation of four-dimensional higher spin gravity based on a covariant Hamiltonian action on an open nine-dimensional Poisson manifold whose boundary consists of the direct product of spacetime and a noncommutative twistor space of S^2 x S^2 topology. The fundamental field is a superconnection consisting of even and odd differential forms valued in the odd and even sectors of a 3-graded associative algebra given by the direct product of an eight-dimensional Frobenius algebra and a higher spin algebra extended by inner Klein operators. The superconnection consists of two one-forms gauging the one-sided actions of the higher spin algebra, two bi-fundamental real forms given by the Weyl zero-form and a new dynamical two-form, an additional set of forms providing a maximal duality extension, and, finally, the Lagrange multipliers required for the covariant Hamiltonian action. In a particular two-form background, the model yields Vasiliev's recently proposed extended higher spin gravity equations, whose interaction terms are accounted for by de Rham closed globally defined forms arising in the dynamical two-form., Comment: 50 pages; v2: 44 pages. Higher spin algebra extended to include inner Klein operators. Appendix A dropped. Trace operation modified and Z_2 projection on the base manifold removed. Comparison with Vasiliev's theory is made precise. Perturbation expansion in holomorphic gauge removed for an expanded treatment in a separate publication. The presentation is somewhat reorganized

In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity., Comment: 17 pages

We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern--Simons theory for Blencowe--Vasiliev higher spin gravity coupled to fractional spin fields and internal gauge potentials. We also examine the model for integer or half-integer fractional spins, where infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras $gl(2l+1)$ or $gl(l|l+1)$ and various real forms thereof., Comment: Published in JHEP. 32 pages, 3 figures

We investigate Lema\^itre-Tolman-Bondi (LTB) models, whose early time evolution and bang time are homogeneous and the distance - redshift relation and local Hubble parameter are inherited from the $\Lambda$CDM model. We show that the obtained LTB models and the $\Lambda$CDM model predict different relative local expansion rates and that the Hubble functions of the models diverge increasingly with redshift. The LTB models show tension between low redshift baryon acoustic oscillation and supernova observations and including Lyman-$\alpha$ forest or cosmic microwave background observations only accentuates the better fit of the $\Lambda$CDM model compared to the LTB model. The result indicates that additional degrees of freedom are needed to explain the observations, for example by renouncing spherical symmetry, homogeneous bang time, negligible effects of pressure, or the early time homogeneity assumption., Comment: 27 pages, 11 figures

We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to any worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model., Comment: 20 pages

We show that the particle states of Maxwell's theory, in $D$ dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality relations which are first order in space-time derivatives. We derive a similar result for the three form in eleven dimensions where such a possibility was first observed in the context of E11. We also give an action formulation for some of the gauge fields. In this paper we give a pedagogical account of the Lorentz and gauge covariant formulation of the irreducible representations of the Poincar\'e group, used previously in higher spin theories, as this plays a key role in our constructions. It is clear that our results can be generalised to any particle., Comment: 37 pages