On Projections to the Pure Spinor Space

A family of covariant non-linear projections from the space of SO(10) Weyl spinors onto the space of pure SO(10) Weyl spinors is presented. The Jacobian matrices of these projections are related to a linear projector which was previously discussed in pure spinor string literature and which maps the antighost to its gauge invariant part. Only one representative of the family leads to a Hermitian Jacobian matrix and can itself be derived from a scalar potential. Comments on the SO(1,9) case are given as well as on the non-covariant version of the projection map. The insight is applied to the ghost action of pure spinor string theory, where the constraints on the fields can be removed using the projection, while introducing new gauge symmetries. This opens the possibility of choosing different gauges which might help to clarify the origin of the pure spinor ghosts. Also the measure of the pure spinor space is discussed from the projection point of view. The appendix contains the discussion of a toy model which served as a guideline for the pure spinor case.Comment: 35+32 pages (main part+ appendix). Changes from version 2 to version 3: Reference [11] added. Equation numbers include now the section number in order to match the published version in JHEP. Changes from version 1 to version 2: Two references added about the derivation of the pure spinor string from a classical action; last equation in footnote 2 rewritten; 3 minor changes in the tex

Emergence of foams from the breakdown of the phase field crystal model

The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foam-like behavior emerges. We characterize this foam phase of the PFC equation and propose a modified PFC equation that may be used for the simulation of foam dynamics. This minimal model reproduces von Neumann's rule for two-dimensional dry foams, and Lifshitz-Slyozov coarsening for wet foams. We also measure the coordination number distribution and find that its second moment is larger than previously-reported experimental and theoretical studies of soap froths, a finding that we attribute to the wetness of the foam increasing with time.Comment: 4 pages, 4 figure

1998 FFTF annual system assessment reports

The health of FFTF systems was assessed assuming a continued facility standby condition. The review was accomplished in accordance with the guidelines of FFTF-EI-083, Plant Evaluation Program. The attached document includes an executive summary of the significant conclusions and assessment reports for each system evaluated

Shadows, currents and AdS fields

Conformal totally symmetric arbitrary spin currents and shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant formulation for such currents and shadow fields is developed. Gauge symmetries are realized by involving the Stueckelberg fields. Realization of global conformal boost symmetries is obtained. Gauge invariant differential constraints for currents and shadow fields are obtained. AdS/CFT correspondence for currents and shadow fields and the respective normalizable and non-normalizable solutions of massless totally symmetric arbitrary spin AdS fields is studied. The bulk fields are considered in modified de Donder gauge that leads to decoupled equations of motion. We demonstrate that leftover on-shell gauge symmetries of bulk fields correspond to gauge symmetries of boundary currents and shadow fields, while the modified de Donder gauge conditions for bulk fields correspond to differential constraints for boundary conformal currents and shadow fields. Breaking conformal symmetries, we find interrelations between the gauge invariant formulation of the currents and shadow fields and the gauge invariant formulation of massive fields.Comment: v3: 31 pages, RevTeX4. Appendix D devoted to modified de Donder gauge in AdS(d+1) x S(d+1) added. Footnotes 10, 21 added. Typos correcte

Emergence of heterogeneity and political organization in information exchange networks

We present a simple model of the emergence of the division of labor and the development of a system of resource subsidy from an agent-based model of directed resource production with variable degrees of trust between the agents. The model has three distinct phases, corresponding to different forms of societal organization: disconnected (independent agents), homogeneous cooperative (collective state), and inhomogeneous cooperative (collective state with a leader). Our results indicate that such levels of organization arise generically as a collective effect from interacting agent dynamics, and may have applications in a variety of systems including social insects and microbial communities.Comment: 10 pages, 6 figure

Production of non-Abelian tensor gauge bosons. Tree amplitudes in generalized Yang-Mills theory and BCFW recursion relation

The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills theory. The amplitudes vanish as complex deformation parameter tends to infinity, so that there is no contribution from the contour at infinity. We derive a generalization of the Parke-Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorhic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. In generalized Yang-Mills theory the tree level n-particle scattering amplitudes with all positive helicities vanish, but tree amplitudes with one negative helicity particle are already nonzero.Comment: 19 pages, LaTex fil

Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields

This review is devoted to the Schwinger and Fronsdal theory of Abelian tensor gauge fields. The theory describes the propagation of free massless gauge bosons of integer helicities and their interaction with external currents. Self-consistency of its equations requires only the traceless part of the current divergence to vanish. The essence of the theory is given by the fact that this weaker current conservation is enough to guarantee the unitarity of the theory. Physically this means that only waves with transverse polarizations are propagating very far from the sources. The question whether such currents exist should be answered by a fully interacting theory. We also suggest an equivalent representation of the corresponding action

A Note on the Classical BRST Symmetry of the Pure Spinor String in a Curved Background

The classical pure spinor version of the heterotic superstring in a supergravity and super Yang-Mills background is considered. We obtain the BRST transformations of the world-sheet fields. They are consistent with the constraints obtained from the nilpotence of the BSRT charge and the holomorphicity of the BRST current.Comment: References adde

Cascade of Complexity in Evolving Predator-Prey Dynamics

We simulate an individual-based model that represents both the phenotype and genome of digital organisms with predator-prey interactions. We show how open-ended growth of complexity arises from the invariance of genetic evolution operators with respect to changes in the complexity, and that the dynamics which emerges is controlled by a non-equilibrium critical point. The mechanism is analogous to the development of the cascade in fluid turbulence.Comment: 5 pages, 3 figures; added comments on system size scaling and turbulence analogy, added error estimates of data collapse parameters. Slightly enhanced from the version which will appear in PR