1,562 research outputs found
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
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
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 to the space of integral forms
where , is the bosonic dimension of the
supermanifold and 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 and
finally discuss Hodge dual fields within the present framework.Comment: 35 page
Direct Algebraic Restoration of Slavnov-Taylor Identities in the Abelian Higgs-Kibble Model
A purely algebraic method is devised in order to recover Slavnov-Taylor
identities (STI), broken by intermediate renormalization. The counterterms are
evaluated order by order in terms of finite amplitudes computed at zero
external momenta. The evaluation of the breaking terms of the STI is avoided
and their validity is imposed directly on the vertex functional. The method is
applied to the abelian Higgs-Kibble model. An explicit mass term for the gauge
field is introduced, in order to check the relevance of nilpotency. We show
that, since there are no anomalies, the imposition of the STI turns out to be
equivalent to the solution of a linear problem. The presence of ST invariants
implies that there are many possible solutions, corresponding to different
normalization conditions. Moreover, we find more equations than unknowns
(over-determined problem). This leads us to the consideration of consistency
conditions, that must be obeyed if the restoration of STI is possible.Comment: 10 pages, Latex and packages amsfonts, amssymb and amsth
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 and we propose a new
variational principle on supermanifolds.Comment: 28 page
BFT embedding of the Green-Schwarz superstring and the pure spinor formalism
We worked out the Batalin-Fradkin-Tyutin (BFT) conversion program of second
class constraints to first class constraints in the GS superstring using light
cone coordinates. By applying this systematic procedure we were able to obtain
a gauge system that is equivalent to the recent model proposed by Berkovits and
Marchioro to relate the GS superstring to the pure spinor formalism.Comment: 12 pages latex2e, v2 typos fixed, v3 published in JHE
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