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.Comment: 36 pages, 10 figures, references added, minor change

Dual-color decompositions at one-loop level in Yang-Mills theory

In this work, we extend the construction of dual color decomposition in Yang-Mills theory to one-loop level, i.e., we show how to write one-loop integrands in Yang-Mills theory to the dual DDM-form and the dual trace-form. In dual forms, integrands are decomposed in terms of color-ordered one-loop integrands for color scalar theory with proper dual color coefficients.In dual DDM decomposition, The dual color coefficients can be obtained directly from BCJ-form by applying Jacobi-like identities for kinematic factors. In dual trace decomposition, the dual trace factors can be obtained by imposing one-loop KK relations, reflection relation and their relation with the kinematic factors in dual DDM-form.Comment: 26 pages,5 figure

Expansion of Einstein-Yang-Mills Amplitude

In this paper, we provide a thorough study on the expansion of single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes, from various different perspectives. Using the gauge invariance principle, we propose a recursive construction, where EYM amplitude with any number of gravitons could be expanded into EYM amplitudes with less number of gravitons. Through this construction, we can write down the complete expansion of EYM amplitude in the basis of color-ordered Yang-Mills amplitudes. As a byproduct, we are able to write down the polynomial form of BCJ numerator, i.e., numerators satisfying the color-kinematic duality, for Yang-Mills amplitude. After the discussion of gauge invariance, we move to the BCFW on-shell recursion relation and discuss how the expansion can be understood from the on-shell picture. Finally, we show how to interpret the expansion from the aspect of KLT relation and the way of evaluating the expansion coefficients efficiently.Comment: 50 pages, 1 figure, Revised versio

Note on symmetric BCJ numerator

We present an algorithm that leads to BCJ numerators satisfying manifestly the three properties proposed by Broedel and Carrasco in [35]. We explicitly calculate the numerators at 4, 5 and 6-points and show that the relabeling property is generically satisfied.Comment: 14 pages, typo in eq.(4.1)is correcte