Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-05-31
Nucl.Phys.B854:193-242,2012
Physics
High Energy Physics
High Energy Physics - Theory
52 pages
Scientific paper
We consider generalization of the Cachazo-Svrcek-Witten (CSW) rules to one-loop amplitudes of N=4 super Yang-Mills theory in a recently developed holonomy formalism in twistor space. We first reconsider off-shell continuation of the Lorentz-invariant Nair measure for the incorporation of loop integrals. We then formulate an S-matrix functional for general amplitudes such that it implements the CSW rules at quantum level. For one-loop MHV amplitudes, the S-matrix functional correctly reproduces the analytic expressions obtained in the Brandhuber-Spence-Travaglini (BST) method. Motivated by this result, we propose a novel regularization scheme by use of an iterated-integral representation of polylogarithms and obtain a set of new analytic expressions for one-loop NMHV and N$^2$MHV amplitudes in a conjectural form. We also briefly sketch how the extension to one-loop non-MHV amplitudes in general can be carried out.
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