Instanton Operators in Five-Dimensional Gauge Theories

TL;DR

This work introduces instanton operators in five-dimensional Yang-Mills as disorder operators that enforce a nonzero instanton flux on surrounding $S^4$, offering a higher-dimensional analogue of monopole operators. By linking these operators to discrete units of six-dimensional momentum, the authors argue they drive the enhancement of the 5D Lorentz symmetry to $SO(1,5)$ at strong coupling and illuminate connections to the six-dimensional $(2,0)$ SCFT via circle compactification. They show that KK-zero correlators are perturbative while nonzero KK modes acquire nonperturbative exponential weights $e^{-\frac{4\pi^2}{g^2} |n| |x|}$, and that instanton operators can be composed with local operators to yield KK modes with momentum along the compact dimension. The results provide a concrete mechanism for UV completion of 5D MSYM, relate 5D physics to M-theory constructions, and suggest broader roles for instanton-like operators in related 5D theories.

Abstract

We discuss instanton operators in five-dimensional gauge theories. These are defined as disorder operators which create a non-vanishing second Chern class on a four-sphere surrounding their insertion point. As such they may be thought of as higher-dimensional analogues of three-dimensional monopole (or `t Hooft) operators. We argue that they play an important role in the enhancement of the Lorentz symmetry for maximally supersymmetric Yang-Mills to SO(1,5) at strong coupling.