Topological M Theory from Pure Spinor Formalism

We construct multiloop superparticle amplitudes in 11d using the pure spinor formalism. We explain how this construction reduces to the superparticle limit of the multiloop pure spinor superstring amplitudes prescription. We then argue that this construction points to some evidence for the existence of a topological M theory based on a relation between the ghost number of the full-fledged supersymmetric critical models and the dimension of the spacetime for topological models. In particular, we show that the extensions at higher orders of the previous results for the tree and one-loop level expansion for the superparticle in 11 dimensions is related to a topological model in 7 dimensions.Comment: harvmac, 28pp. v2: Assorted english correction

Higher-loop amplitudes in the non-minimal pure spinor formalism

We analyze the properties of the non-minimal pure spinor formalism. We show that Siegel gauge on massless vertex operators implies the primary field constraint and the level-matching condition in closed string theory by reconstructing the integrated vertex operator representation from the unintegrated ones. The pure spinor integration in the non-minimal formalism needs a regularisation. To this end we introduce a new regulator for the pure spinor integration and an extension of the regulator to allow for the saturation of the fermionic d-zero modes to all orders in perturbation. We conclude with a preliminary analysis of the properties of the four-graviton amplitude to all genus order.Comment: v1: harvmac format. 28 pages. No figures. v2: added references and typos corrected. Expanded discussion of the zero mode counting and the vanishing condition of amplitudes. v3: minor correction

Hodge Dualities on Supermanifolds

We discuss the cohomology of superforms and integral forms from a new perspective based on a recently proposed Hodge dual operator. We show how the superspace constraints (a.k.a. rheonomic parametrisation) are translated from the space of superforms $\Omega^{(p|0)}$ to the space of integral forms $\Omega^{(p|m)}$ where $0 \leq p \leq n$, $n$ is the bosonic dimension of the supermanifold and $m$ its fermionic dimension. We dwell on the relation between supermanifolds with non-trivial curvature and Ramond-Ramond fields, for which the Laplace-Beltrami differential, constructed with our Hodge dual, is an essential ingredient. We discuss the definition of Picture Lowering and Picture Raising Operators (acting on the space of superforms and on the space of integral forms) and their relation with the cohomology. We construct non-abelian curvatures for gauge connections in the space $\Omega^{(1|m)}$ and finally discuss Hodge dual fields within the present framework.Comment: 35 page

Novel Free Differential Algebras for Supergravity

We develop the theory of Free Integro-Differential Algebras (FIDA) extending the powerful technique of Free Differential Algebras constructed by D. Sullivan. We extend the analysis beyond the superforms to integral- and pseudo-forms used in supergeometry. It is shown that there are novel structures that might open the road to a deeper understanding of the geometry of supergravity. We apply the technique to some models as an illustration and we provide a complete analysis for D=11 supergravity. There, it is shown how the Hodge star operator for supermanifolds can be used to analyze the set of cocycles and to build the corresponding FIDA. A new integral form emerges which plays the role of the truly dual to 4-form $F^{(4)}$ and we propose a new variational principle on supermanifolds.Comment: 28 page

Superstrings on AdS_4 x CP^3 from Supergravity

We derive from a general formulation of pure spinor string theory on type IIA backgrounds the specific form of the action for the AdS_4 x P^3 background. We provide a complete geometrical characterization of the structure of the superfields involved in the action.Comment: 32 pages, Latex, no figure