arXiv subjects

Chih-Hao Fu

Publications and source records attributed to Chih-Hao Fu.

26 records · Page 2Linked to original sources

arXiv2012

Note on Cyclic Sum and Combination Sum of Color-ordered Gluon Amplitudes

Continuing our previous study \cite{Du:2011se} of permutation sum of color ordered tree amplitudes of gluons, in this note, we prove the large-$z$ behavior of their cyclic sum and the combination of cyclic and permutation sums under BCFW deformation. Unlike the permutation sum, the study of cyclic sum and the combination of cyclic and permutation sums is much more difficult. By using the generalized Bern-Carrasco-Johansson (BCJ) relation, we have proved the boundary behavior of cyclic sum with nonadjacent BCFW deformation. The proof of cyclic sum with adjacent BCFW deformation is a little bit simpler, where only Kleiss-Kuijf (KK) relations are needed. Finally we have presented a new observation for partial-ordered permutation sum and applied it to prove the boundary behavior of combination sum with cyclic and permutation.

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arXiv2011

Note on Permutation Sum of Color-ordered Gluon Amplitudes

In this note we show that under BCFW-deformation the large z behavior of permutation sum of color-ordered gluon amplitudes found by Boels and Isermann in arxiv:1109.5888 can be simply understood from the well known Kleiss-Kuijf relation and Bern-Carrasco-Johansson relation.

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arXiv2011

BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory

We present a field theoretical proof of the conjectured KLT relation which states that the full tree-level scattering amplitude of gluons can be written as a product of color-ordered amplitude of gluons and color-ordered amplitude of scalars with only cubic vertex. To give a proof we establish the KK relation and BCJ relation of color-ordered scalar amplitude using BCFW recursion relation with nonzero boundary contributions. As a byproduct, an off-shell version of fundamental BCJ relation is proved, which plays an important role in our work.

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arXiv2010

New N=4 SYM Path Integral

Using Lorentz covariant spinor helicity formalism we reorganize the unitary scalar superfield light-cone path integral for the N=4 supersymmetric Yang-Mills theory. In new variables in the chiral Fourier superspace the quadratic and cubic parts of the classical action have manifest Lorentz, kinematical and dynamical supersymmetry, with the exception of terms which contribute only to the contact terms in the supergraphs with propagators shrinking to a point. These terms have the same structure as supergraphs with quartic light-cone vertices, which break dynamical supersymmetry. We present evidence that all complicated terms breaking dynamical supersymmetry have to cancel and therefore can be omitted. It is plausible that the new form of the path integral leads to a set of relatively simple unitarity based rules with manifest N=4 supersymmetry.

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arXiv2010

Generating MHV super-vertices in light-cone gauge

We constructe the $\mathcal{N}=1$ SYM lagrangian in light-cone gauge using chiral superfields instead of the standard vector superfield approach and derive the MHV lagrangian. The canonical transformations of the gauge field and gaugino fields are summarised by the transformation condition of chiral superfields. We show that $\mathcal{N}=1$ MHV super-vertices can be described by a formula similar to that of the $\mathcal{N}=4$ MHV super-amplitude. In the discussions we briefly remark on how to derive Nair's formula for $\mathcal{N}=4$ SYM theory directly from light-cone lagrangian.

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arXiv2009

The MHV lagrangian vertices and the Parke-Taylor formula

We explicitly calculate the vertices of the MHV-rules lagrangian in 4-dimensions. This proves that the vertices in the lagrangian obtained by a canonical transformation from light-cone Yang-Mills theory coincide to all order with the Parke-Taylor formula, filling the gap originally left in the lagrangian derivation of the CSW rules.

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arXiv2009

S-matrix equivalence restored

The canonical transformation that maps light-cone Yang-Mills theory to a Lagrangian description of the MHV rules is non-local, consequently the two sets of fields do not necessarily generate the same S-matrix. By deriving a new recursion relation for the canonical transformation expansion coefficients, we find a direct map between these coefficients and tree level light-cone diagrams. We use this to show that, at least up to one-loop with dimensionally regularised MHV vertices, the only difference is the omission of the one-loop amplitudes in which all gluons have positive helicity.

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arXiv2007

S-Matrix Equivalence Theorem Evasion and Dimensional Regularisation with the Canonical MHV Lagrangian

We demonstrate that the canonical change of variables that yields the MHV lagrangian, also provides contributions to scattering amplitudes that evade the equivalence theorem. This `ET evasion' in particular provides the tree-level (-++) amplitude, which is non-vanishing off shell, or on shell with complex momenta or in (2,2) signature, and is missing from the MHV (aka CSW) rules. At one loop there are ET-evading diagrammatic contributions to the amplitudes with all positive helicities. We supply the necessary regularisation in order to define these contributions (and quantum MHV methods in general) by starting from the light-cone Yang-Mills lagrangian in D dimensions and making a canonical change of variables for all D-2 transverse degrees of freedom of the gauge field. In this way, we obtain dimensionally regularised three- and four-point MHV amplitudes. Returning to the one-loop (++++) amplitude, we demonstrate that its quadruple cut coincides with the known result, and show how the original light-cone Yang-Mills contributions can in fact be algebraically recovered from the ET-evading contributions. We conclude that the canonical MHV lagrangian, supplemented with the extra terms brought to correlation functions by the non-linear field transformation, provide contributions which are just a rearrangement of those from light-cone Yang-Mills and thus coincide with them both on and off shell.

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