Supersymmetrizing 5d instanton operators

TL;DR

The paper addresses how to define supersymmetric instanton operators in five-dimensional Yang-Mills theories, where such theories can exhibit fixed points and symmetry enhancements. It introduces a five-dimensional generalization of a topological twist by identifying the $SU(2)_R$ R-symmetry connection with the spin connection, yielding conformal Killing spinors on $S^4$ and allowing a supersymmetric embedding of Yang monopole configurations in $\mathbb{R}^5$. Explicit SUSY spinors are given, e.g., $\epsilon^1 = c\,\sqrt{r}\,(1000)$ and $\epsilon^2 = c\,\sqrt{r}\,(0100)$, with $\Gamma_5 \epsilon^i = \epsilon^i$, and the background $SU(2)_R$ bundle carries a nontrivial second Chern class $\int_{S^4} R_i^{\ j} \wedge R_j^{\ i} = 8\pi^2$, effectively forming a background Yang monopole. The construction relates to a conformal map between $\mathbb{R}^5$ and $\mathbb{R} \times S^4$, offering a controlled framework to study supersymmetric instanton operators and potential symmetry enhancements in 5d gauge theories with connections to higher-dimensional theories.

Abstract

We construct a supersymmetric version of instanton operators in five-dimensional Yang-Mills theories. This is possible by considering a five-dimensional generalization of the familiar four-dimensional topologically twisted theory, where the gauge configurations corresponding to instanton operators are supersymmetric.