Abstract
Recently, loop integrands for certain Yang-Mills scattering amplitudes and correlation functions have been shown to be systematically expressible in dlog form, raising the possibility that these loop integrals can be performed directly without Feynman parameters. We do so here to give a new description of the planar 1-loop MHV amplitude in N = 4 super Yang-Mills theory. We explicitly incorporate the standard Feynman i epsilon prescription into the integrands. We find that the generic MHV diagram contributing to the 1-loop MHV amplitude, known as Kermit, is dual conformal invariant up to the choice of reference twistor explicit in our axial gauge (the generic MHV diagram was already known to be finite). The new formulae for the amplitude are nontrivially related to previous ones in the literature. The divergent diagrams are evaluated using mass regularization. Our techniques extend directly to higher loop diagrams, and we illustrate this by sketching the evaluation of a non-trivial 2-loop example. We expect this to lead to a simple and efficient method for computing amplitudes and correlation functions with less supersymmetry and without the assumption of planarity.
Highlights
We review the basic definitions and set up the notation for the rest of the paper
We find that the generic MHV diagram contributing to the 1-loop MHV amplitude, known as Kermit, is dual conformal invariant up to the choice of reference twistor explicit in our axial gauge
In appendix A, we show that our result for the generic Wilson-loop diagram is equivalent to the result for the 1-loop MHV amplitude previously obtained in [5] using unitarity methods applied to the MHV diagram formalism
Summary
We review the basic definitions and set up the notation for the rest of the paper. The dual superconformal symmetry of the amplitudes can be made more manifest by writing the polygon in terms of (momentum) supertwistors: ZiA, χai = λiα, μαi , χai. They transform in the fundamental representation of the dual superconformal group SU(2, 2|4) and relate to the region supermomenta by the ‘incidence relations’. Note that they differ by a factor of i from those used in [31] These depend on the reference twistor, and only those combinations that are independent of the choice of the scalings of the Zi are fully (dual-) conformal invariant.
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