6d Dual Conformal Symmetry and Minimal Volumes in AdS

TL;DR

This paper explores the implications of dual conformal symmetry in six dimensions, revealing its role in fixing one-loop amplitudes, suggesting a higher-derivative Lagrangian, and connecting to holographic minimal volume M2-branes in AdS space.

Contribution

It demonstrates that 6d dual conformal symmetry uniquely constrains the one-loop 4-point amplitude and extends holographic methods to minimal volume M2-branes, proposing a potential all-loop amplitude formula.

Findings

6d dual conformal symmetry fixes the one-loop 4-point integrand.

The amplitude structure hints at a Lagrangian with more than two derivatives.

Holographic analysis involves minimal volume M2-branes in AdS space.

Abstract

The S-matrix of a theory often exhibits symmetries which are not manifest from the viewpoint of its Lagrangian. For instance, powerful constraints on scattering amplitudes are imposed by the dual conformal symmetry of planar 4d $\mathcal{N}=4$ super Yang-Mills theory and the ABJM theory. Motivated by this, we investigate the consequences of dual conformal symmetry in six dimensions, which may provide useful insight into the worldvolume theory of M5-branes (if it enjoys such a symmetry). We find that 6d dual conformal symmetry uniquely fixes the integrand of the one-loop 4-point amplitude, and its structure suggests a Lagrangian with more than two derivatives. On integrating out the loop momentum in $6-2 \epsilon$ dimensions, the result is very similar to the corresponding amplitude of $\mathcal{N}=4$ super Yang-Mills theory. We confirm this result holographically by generalizing the Alday-Maldacena solution for a minimal area string in Anti-de Sitter space to a minimal volume M2-brane ending on pillow-shaped Wilson surface in the boundary whose seams correspond to a null-polygonal Wilson loop. This involves careful treatment of a prefactor which diverges as $1/\epsilon$, and we comment on its possible interpretation. We also study 2-loop 4-point integrands with 6d dual conformal symmetry and speculate on the existence of an all-loop formula for the 4-point amplitude.