Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory

TL;DR

The paper proves that 1-loop NMHV n-point amplitudes in planar ${\cal N}=4$ SYM are dual conformal covariant after IR regularization, for all $n$, by constructing an explicit cross-ratio representation of the NMHV ratio ${\cal R}_{n,1}^{\rm NMHV}$ and proving IR finiteness. It achieves this by decomposing amplitudes into scalar box integrals, deriving box-coefficient structures in terms of dual-invariant $R_{ijk}$, and then performing cyclicity-based refinements and linear-relations to obtain manifestly dual-conformal, IR-finite coefficients ${\cal S}$ expressed through dual conformal cross-ratios. The work also proves that individual box coefficients are covariant under dual (super)conformal transformations, extending the covariance to all one-loop N^kMHV amplitudes, and discusses the relation to dual superconformal symmetry and potential extensions to higher $k$. Overall, the results solidify the dual-conformal structure of one-loop amplitudes in ${\cal N}=4$ SYM and provide explicit cross-ratio formulas that can guide further analytic and numerical studies, including higher-loop and higher-$k$ explorations.

Abstract

We prove that 1-loop n-point NMHV superamplitudes in N=4 SYM theory are dual conformal covariant for all numbers n of external particles (after regularization and subtraction of IR divergences). This property was previously established for n < 10 in arXiv:0808.0491. We derive an explicit representation of these superamplitudes in terms of dual conformal cross-ratios. We also show that all the 1-loop `box coefficients' obtained from maximal cuts of N^kMHV n-point functions are covariant under dual conformal transformations.

Figures (1)

• Figure 1: A general box diagram with tree subamplitudes $A$, $B$, $C$, $D$. There is a zone variable $x_i$ between each pair of external lines. Four of these are indicated. The zone vector $x_0$ is discussed in Sec. \ref{['secDan']}.