6d dual conformal symmetry and minimal volumes in AdS

Bhattacharya, Jyotirmoy; Lipstein, Arthur E.

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 N=4N=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 − 2ϵ dimensions, the result is very similar to the corresponding amplitude of N=4N=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 a pillow-shaped surface in the boundary whose seams correspond to a null-polygon. This involves careful treatment of a prefactor which diverges as 1/ϵ, 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.

Citation

Bhattacharya, J., & Lipstein, A. E. (2016). 6d dual conformal symmetry and minimal volumes in AdS. Journal of High Energy Physics, 2016(12), Article 105. https://doi.org/10.1007/jhep12%282016%29105

• Journal Article Type: Article
• Acceptance Date: Dec 12, 2016
• Online Publication Date: Dec 20, 2016
• Publication Date: Dec 20, 2016
• Deposit Date: Jan 30, 2017
• Publicly Available Date: Jan 30, 2017
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2016
• Issue: 12
• Article Number: 105
• DOI: https://doi.org/10.1007/jhep12%282016%29105
• Public URL: https://durham-repository.worktribe.com/output/1366379
• Related Public URLs: https://arxiv.org/abs/1611.02179