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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

We show that the partition function on a generalised conifold $C_{m,n}$ with ${m+n \choose m}$ crepant resolutions can be equivalently computed on the compound du Val singularity $A_{m+n-1}\times \mathbb C$ with a unique crepant resolution., Comment: v2 has small corrections, has improved exposition. Revised version to appear in: "Journal of Mathematical Physics"

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)

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 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

Spinor-valued one-forms (Rarita-Schwinger fields) are normally used in the context of supergravity, where they describe spin 3/2 particles (gravitinos). Indeed, when decomposed into irreducible representations of the Lorentz group such a field contains both a spin 1/2 and a spin 3/2 component, and the Rarita-Schwinger Lagrangian is designed to make only the spin 3/2 propagate. We point out that the opposite construction is also possible, and give a spinor-valued one-form field Lagrangian that describes a propagating spin 1/2 particle., Comment: 23 pages, no figures

We revisit an old idea that gravity can be unified with Yang-Mills theory by enlarging the gauge group of gravity formulated as gauge theory. Our starting point is an action that describes a generally covariant gauge theory for a group G. The Minkowski background breaks the gauge group by selecting in it a preferred gravitational SU(2) subgroup. We expand the action around this background and find the spectrum of linearized theory to consist of the usual gravitons plus Yang-Mills fields charged under the centralizer of the SU(2) in G. In addition, there is a set of Higgs fields that are charged both under the gravitational and Yang-Mills subgroups. These fields are generically massive and interact with both gravity and Yang-Mills sector in the standard way. The arising interaction of the Yang-Mills sector with gravity is also standard. Parameters such as the Yang-Mills coupling constant and Higgs mass arise from the potential function defining the theory. Both are realistic in the sense explained in the paper., Comment: 61 pages, no figures (v2) some typos corrected