3,237 research outputs found
Assessment of the Quality of Safety Cases: A Research Preview
Proceedings of the 25th International Working Conference, REFSQ 2019, Essen, Germany, March 18–21, 2019.[Context and motivation] Safety-critical systems in application domains such as aerospace, automotive, healthcare, and railway are subject to assurance processes to provide confidence that the systems do not pose undue risks to people, property, or the environment. The development of safety cases is usually part of these processes to justify that a system satisfies its safety requirements and thus is dependable. [Question/problem] Although safety cases have been used in industry for over two decades, their management still requires improvement. Important weaknesses have been identified and means to assess the quality of safety cases are limited. [Principal ideas/results] This paper presents a research preview on the assessment of the quality of safety cases. We explain how the area should develop and present our preliminary work towards enabling the assessment with Verification Studio, an industrial tool for system artefact quality analysis. [Contribution] The insights provided allow researchers and practitioners to gain an understanding of why safety case quality requires further investigation, what aspects must be considered, and how quality assessment could be performed in practice.The research leading to this paper has received funding from the AMASS project (H2020-ECSEL ID 692474; Spain’s MINECO ref. PCIN-2015-262). We also thank REFSQ reviewers for their valuable comments to improve the paper
Solution to the Ward Identities for Superamplitudes
Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a
supersymmetric field theory. We solve these Ward identities for (Next-to)^K MHV
amplitudes of the maximally supersymmetric N=4 and N=8 theories. The resulting
superamplitude is written in a new, manifestly supersymmetric and R-invariant
form: it is expressed as a sum of very simple SUSY and SU(N)_R-invariant
Grassmann polynomials, each multiplied by a "basis amplitude". For (Next-to)^K
MHV n-point superamplitudes the number of basis amplitudes is equal to the
dimension of the irreducible representation of SU(n-4) corresponding to the
rectangular Young diagram with N columns and K rows. The linearly independent
amplitudes in this algebraic basis may still be functionally related by
permutation of momenta. We show how cyclic and reflection symmetries can be
used to obtain a smaller functional basis of color-ordered single-trace
amplitudes in N=4 gauge theory. We also analyze the more significant reduction
that occurs in N=8 supergravity because gravity amplitudes are not ordered. All
results are valid at both tree and loop level.Comment: 29 pages, published versio
Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
Infrared equations and dual conformal constraints arise as consistency
conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions
are linear relations between leading singularities, which can be computed in
the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently.
Examples for infrared equations have been shown to be implied by global residue
theorems in the Grassmannian picture. Both dual conformal constraints and
infrared equations are mapped explicitly to global residue theorems for
one-loop next-to-maximally-helicity-violating amplitudes. In addition, the
identity relating the BCFW and its parity-conjugated form of tree-level
amplitudes, is shown to emerge from a particular combination of global residue
theorems.Comment: 21 page
Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
An on-shell formalism for the computation of S-matrices of SYM theories in
three spacetime dimensions is presented. The framework is a generalization of
the spinor-helicity formalism in four dimensions. The formalism is applied to
establish the manifest SO(N) covariance of the on-shell superalgebra relevant
to N =2,4 and 8 SYM theories in d=3. The results are then used to argue for the
SO(N) invariance of the S-matrices of these theories: a claim which is proved
explicitly for the four-particle scattering amplitudes. Recursion relations
relating tree amplitudes of three-dimensional SYM theories are shown to follow
from their four-dimensional counterparts. The results for the four-particle
amplitudes are verified by tree-level perturbative computations and a unitarity
based construction of the integrand corresponding to the leading perturbative
correction is also presented for the N=8 theory. For N=8 SYM, the manifest
SO(8) symmetry is used to develop a map between the color-ordered amplitudes of
the SYM and superconformal Chern-Simons theories, providing a direct connection
between on-shell observables of D2 and M2-brane theories.Comment: 28 page
Unraveling L_{n,k}: Grassmannian Kinematics
It was recently proposed that the leading singularities of the S-Matrix of N
= 4 super Yang-Mills theory arise as the residues of a contour integral over a
Grassmannian manifold, with space-time locality encoded through residue
theorems generalizing Cauchy's theorem to more than one variable. We provide a
method to identify the residue corresponding to any leading singularity, and we
carry this out very explicitly for all leading singularities at tree level and
one-loop. We also give several examples at higher loops, including all generic
two-loop leading singularities and an interesting four-loop object. As a
special case we consider a 12-pt N^4MHV leading singularity at two loops that
has a new kinematic structure involving double square roots. Our analysis
results in a simple picture for how the topological structure of loop graphs is
reflected in various substructures within the Grassmannian.Comment: 26+11 page
The S-Matrix in Twistor Space
The simplicity and hidden symmetries of (Super) Yang-Mills and (Super)Gravity
scattering amplitudes suggest the existence of a "weak-weak" dual formulation
in which these structures are made manifest at the expense of manifest
locality. We suggest that this dual description lives in (2,2) signature and is
naturally formulated in twistor space. We recast the BCFW recursion relations
in an on-shell form that begs to be transformed into twistor space. Our twistor
transformation is inspired by Witten's, but differs in treating twistor and
dual twistor variables more equally. In these variables the three and
four-point amplitudes are amazingly simple; the BCFW relations are represented
by diagrammatic rules that precisely define the "twistor diagrams" of Andrew
Hodges. The "Hodges diagrams" for Yang-Mills theory are disks and not trees;
they reveal striking connections between amplitudes and suggest a new form for
them in momentum space. We also obtain a twistorial formulation of gravity. All
tree amplitudes can be combined into an "S-Matrix" functional which is the
natural holographic observable in asymptotically flat space; the BCFW formula
turns into a quadratic equation for this "S-Matrix", providing a holographic
description of N=4 SYM and N=8 Supergravity at tree level. We explore loop
amplitudes in (2,2) signature and twistor space, beginning with a discussion of
IR behavior. We find that the natural pole prescription renders the amplitudes
well-defined and free of IR divergences. Loop amplitudes vanish for generic
momenta, and in twistor space are even simpler than their tree-level
counterparts! This further supports the idea that there exists a sharply
defined object corresponding to the S-Matrix in (2,2) signature, computed by a
dual theory naturally living in twistor space.Comment: V1: 46 pages + 23 figures. Less telegraphic abstract in the body of
the paper. V2: 49 pages + 24 figures. Largely expanded set of references
included. Some diagrammatic clarifications added, minor typo fixe
A manifestly MHV Lagrangian for N=4 Yang-Mills
We derive a manifestly MHV Lagrangian for the N=4 supersymmetric Yang-Mills
theory in light-cone superspace. This is achieved by constructing a canonical
redefinition which maps the N=4 superfield and its conjugate to a new pair of
superfields. In terms of these new superfields the N=4 Lagrangian takes a
(non-polynomial) manifestly MHV form, containing vertices involving two
superfields of negative helicity and an arbitrary number of superfields of
positive helicity. We also discuss constraints satisfied by the new
superfields, which ensure that they describe the correct degrees of freedom in
the N=4 supermultiplet. We test our derivation by showing that an expansion of
our superspace Lagrangian in component fields reproduces the correct gluon MHV
vertices.Comment: 37 pages, 1 figure. v2: minor changes, references adde
A note on the boundary contribution with bad deformation in gauge theory
Motivated by recently progresses in the study of BCFW recursion relation with
nonzero boundary contributions for theories with scalars and
fermions\cite{Bofeng}, in this short note we continue the study of boundary
contributions of gauge theory with the bad deformation. Unlike cases with
scalars or fermions, it is hard to use Feynman diagrams directly to obtain
boundary contributions, thus we propose another method based on the SYM theory. Using this method, we are able to write down a useful
on-shell recursion relation to calculate boundary contributions from related
theories. Our result shows the cut-constructibility of gauge theory even with
the bad deformation in some generalized sense.Comment: 16 pages, 7 figure
Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
We calculate form factors of half-BPS operators in N=4 super Yang-Mills
theory at tree level and one loop using novel applications of recursion
relations and unitarity. In particular, we determine the expression of the
one-loop form factors with two scalars and an arbitrary number of
positive-helicity gluons. These quantities resemble closely the MHV scattering
amplitudes, including holomorphicity of the tree-level form factor, and the
expansion in terms of two-mass easy box functions of the one-loop result. Next,
we compare our result for these form factors to the calculation of a particular
periodic Wilson loop at one loop, finding agreement. This suggests a novel
duality relating form factors to periodic Wilson loops.Comment: 26 pages, 10 figures. v2: typos fixed, comments adde
Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
We prove that 1-loop n-point NMHV superamplitudes in N=4 SYM theory are dual
conformal covariant for all numbers n of external particles (after
regularization and subtraction of IR divergences). This property was previously
established for n < 10 in arXiv:0808.0491. We derive an explicit representation
of these superamplitudes in terms of dual conformal cross-ratios. We also show
that all the 1-loop `box coefficients' obtained from maximal cuts of N^kMHV
n-point functions are covariant under dual conformal transformations.Comment: 20 pages, 2 figure
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