Higher representations for extended operators

Understand

It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups.

• The purpose of this paper is to generalise this statement to extended operators such as line and surface defects.
• We explain that $(n-1)$-dimensional operators transform in $n$-representations of a finite invertible or group-like symmetry and thoroughly explore this statement for $n = 1,2,3$.
• We therefore propose higher representation theory as the natural framework to describe the action of symmetries on the extended operator content in quantum field theory.