Dual Conformal Structure Beyond the Planar Limit.

Zvi Bern,Mao Zeng,Michael Enciso,Chia-Hsien Shen

doi:10.1103/physrevlett.121.121603

Zvi Bern, Mao Zeng + Show 2 more

Open Access

https://doi.org/10.1103/physrevlett.121.121603

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Journal: Physical Review Letters	Publication Date: Sep 21, 2018
Citations: 25	License type: CC BY 4.0

Affiliation: University of California, Los Angeles

Abstract

The planar scattering amplitudes of N=4 super-Yang-Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at infinity. Recent work shows in various nontrivial examples that the simple analytic properties of the planar sector survive into the nonplanar sector, but this has yet to be understood from underlying symmetries. Here, we explicitly show that for an infinite class of nonplanar integrals that covers all subleading-color contributions to the two-loop four- and five-point amplitudes of N=4 super-Yang-Mills theory, symmetries analogous to dual conformal invariance exist. A natural conjecture is that this continues to all amplitudes of the theory at any loop order.

Highlights

Introduction.—Recent years have seen significant advances in constructing scattering amplitudes, especially for planar N 1⁄4 4 super-Yang-Mills (SYM) theory
Grassmannian [9], which culminated in the geometric concept of the amplituhedron [10]. Some of these advances have been helpful in quantum chromodynamics relevant for collider physics, including improved ways for dealing with polylogarithms that arise in multiloop computations [11] and for finding good choices [12,13,14] of integral bases that simplify their evaluation
It is unclear how to define dual conformal symmetry in the nonplanar sector given the lack of dual variables to define the symmetry

Summary

Introduction

Introduction.—Recent years have seen significant advances in constructing scattering amplitudes, especially for planar N 1⁄4 4 super-Yang-Mills (SYM) theory. [23], we answer this question affirmatively and demonstrate that the integrands Ij in (2) encoding the simple analytic structure of the full two-loop four- and fivepoint amplitudes all have hidden symmetries related to dual conformal invariance. This implies that locality is maintained for planar loop integrals under dual conformal transformations and allows us to construct simple functions that are invariant.

Results

Conclusion