Yangian Symmetry in Five Dimensions

TL;DR

This paper constructs a Yangian symmetry for 5d superconformal theories derived from 6d $(2,0)$ theory, suggesting potential exact solvability in the planar limit through an infinite-dimensional algebraic structure.

Contribution

It introduces a novel Yangian symmetry representation for 5d superconformal groups using 6d supertwistors, indicating integrability of these theories.

Findings

Yangian symmetry extends the 5d superconformal group.

Potential for exact solvability of 5d theories in the planar limit.

Connection between 6d $(2,0)$ theory reductions and integrable models.

Abstract

Quantum gravity in AdS$_7 \times$S$^4$ is dual to a 6d superconformal field theory, known as the 6d $(2,0)$ theory, which is very challenging to describe because it lacks a conventional Lagrangian description. On the other hand, certain null reductions of the 6d $(2,0)$ theory give rise to 5d Lagrangian theories with $SU(1,3)$ spacetime symmetry, $SO(5)$ R-symmetry, and 24 supercharges. This appears to be closely related to the superconformal group of a 3d superconformal Chern-Simons theory known as the ABJM theory, which is believed to be integrable in the planar limit, if one exchanges the role of conformal and R-symmetry. In this note, we construct a representation of the 5d superconformal group using 6d supertwistors and show that it admits an infinite dimensional extension known as Yangian symmetry, which opens up the possiblity that these 5d theories are exactly solvable in the planar limit.