OPE of line defects in 5d $E_n$ SCFT

TL;DR

This paper computes the 5d superconformal index with ray-like defects in $E_n$ SCFTs, revealing non-trivial operator charges and OPE structures of defects in these theories.

Contribution

It introduces the computation of the ray index for adjoint Wilson rays in 5d $E_n$ SCFTs, uncovering non-trivial charge assignments and defect interactions.

Findings

Operators have non-trivial charges under the $E_n$ center.

Charge under the center is twice that of elementary ray operators.

Indicates a non-trivial OPE between UV ray-like defects.

Abstract

5d ray index is the 5d superconformal index in the presence of a ray-like defect. An elementary ray defect flows to a fundamental Wilson ray in IR gauge theory. In 5d $\mathcal{N}=1$ superconformal field theory(SCFT) with $E_n$ global symmetry, we compute the ray index associated with an adjoint Wilson ray. We show that the operators that appear in the index are non-trivially charged under the center of the global symmetry $E_n$. The charge under the center being twice compared with the center charge carried by the elementary ray operator indicates a non-trivial OPE between the ray-like defects in the UV SCFT.