Magnetism in clean energy and environment

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The Grassmannian Origin Of Dual Superconformal Invariance

A dual formulation of the S Matrix for N=4 SYM has recently been presented, where all leading singularities of n-particle N^{k-2}MHV amplitudes are given as an integral over the Grassmannian G(k,n), with cyclic symmetry, parity and superconformal invariance manifest. In this short note we show that the dual superconformal invariance of this object is also manifest. The geometry naturally suggests a partial integration and simple change of variable to an integral over G(k-2,n). This change of variable precisely corresponds to the mapping between usual momentum variables and the "momentum twistors" introduced by Hodges, and yields an elementary derivation of the momentum-twistor space formula very recently presented by Mason and Skinner, which is manifestly dual superconformal invariant. Thus the G(k,n) Grassmannian formulation allows a direct understanding of all the important symmetries of N=4 SYM scattering amplitudes.Comment: 9 page

Efficient Communication of Sensors Monitoring Overhead Transmission Lines

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A Schwarz lemma for complete Riemannian manifolds

Author name used in this publication: Leung-Fu CheungVersion of RecordPublishe

The second variation formula for exponentially harmonic maps

Author name used in this publication: Leung-Fu CheungVersion of RecordPublishe

On correlation functions of Wilson loops, local and non-local operators

We discuss and extend recent conjectures relating partial null limits of correlation functions of local gauge invariant operators and the expectation value of null polygonal Wilson loops and local gauge invariant operators. We point out that a particular partial null limit provides a strategy for the calculation of the anomalous dimension of short twist-two operators at weak and strong coupling.Comment: 29 pages, 8 figure

No triangles on the moduli space of maximally supersymmetric gauge theory

Maximally supersymmetric gauge theory in four dimensions has a remarkably simple S-matrix at the origin of its moduli space at both tree and loop level. This leads to the question what, if any, of this structure survives at the complement of this one point. Here this question is studied in detail at one loop for the branch of the moduli space parameterized by a vacuum expectation value for one complex scalar. Motivated by the parallel D-brane picture of spontaneous symmetry breaking a simple relation is demonstrated between the Lagrangian of broken super Yang-Mills theory and that of its higher dimensional unbroken cousin. Using this relation it is proven both through an on- as well as an off-shell method there are no so-called triangle coefficients in the natural basis of one-loop functions at any finite point of the moduli space for the theory under study. The off-shell method yields in addition absence of rational terms in a class of theories on the Coulomb branch which includes the special case of maximal supersymmetry. The results in this article provide direct field theory evidence for a recently proposed exact dual conformal symmetry motivated by the AdS/CFT correspondence.Comment: 39 pages, 4 figure

On BCFW shifts of integrands and integrals

In this article a first step is made towards the extension of Britto-Cachazo-Feng-Witten (BCFW) tree level on-shell recursion relations to integrands and integrals of scattering amplitudes to arbitrary loop order. Surprisingly, it is shown that the large BCFW shift limit of the integrands has the same structure as the corresponding tree level amplitude in any minimally coupled Yang-Mills theory in four or more dimensions. This implies that these integrands can be reconstructed from a subset of their `single cuts'. The main tool is powercounting Feynman graphs in a special lightcone gauge choice employed earlier at tree level by Arkani-Hamed and Kaplan. The relation between shifts of integrands and shifts of its integrals is investigated explicitly at one loop. Two particular sources of discrepancy between the integral and integrand are identified related to UV and IR divergences. This is cross-checked with known results for helicity equal amplitudes at one loop. The nature of the on-shell residue at each of the single-cut singularities of the integrand is commented upon. Several natural conjectures and opportunities for further research present themselves.Comment: 43 pages, 6 figures, v2: minor improvement in exposition, typos fixed, bibliography update

Boundary Contributions Using Fermion Pair Deformation

Continuing the study of boundary BCFW recursion relation of tree level amplitudes initiated in \cite{Feng:2009ei}, we consider boundary contributions coming from fermion pair deformation. We present the general strategy for these boundary contributions and demonstrate calculations using two examples, i.e, the standard QCD and deformed QCD with anomalous magnetic momentum coupling. As a by-product, we have extended BCFW recursion relation to off-shell gluon current, where because off-shell gluon current is not gauge invariant, a new feature must be cooperated.Comment: 26 pages, 4 figure

Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions

The spinor helicity formalism in four dimensions has become a very useful tool both for understanding the structure of amplitudes and also for practical numerical computation of amplitudes. Recently, there has been some discussion of an extension of this formalism to higher dimensions. We describe a particular implementation of the spinor-helicity method in ten dimensions. Using this tool, we study the tree-level S-matrix of ten dimensional super Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry. Implications for four-dimensional computations are discussed.Comment: 24 pages, 1 figure