An Index for Ray Operators in 5d $E_n$ SCFTs

Understand

We construct an index for BPS operators supported on a ray in five dimensional superconformal field theories with exceptional global symmetries.

• We compute the $E_n$ representations (for $n=2,\dots,7$) of operators of low spin, thus verifying that while the expression for the index is only SO$(2n-2)\times$U(1) invariant, the index itself exhibits the full $E_n$ symmetry (at least up to the order we expanded).
• The ray operators we studied in 5d can be viewed as generalizations of operators constructed in a Yang-Mills theory with fundamental matter by attaching an open Wilson line to a quark.
• For $n\le 7$, in contrast to local operators, they carry nontrivial charge under the $\mathbb{Z}_{9-n}\subset E_n$ center of the global symmetry.