Instanton Worldlines in Five-Dimensional $\Omega$-Deformed Gauge Theory

TL;DR

This paper explores a five-dimensional supersymmetric gauge theory with an $ ext{SU}(1,3)$ symmetry, introducing an $ ext{Omega}$-deformed anti-self-dual constraint, and constructs explicit solutions representing anti-instanton worldlines.

Contribution

It introduces a novel $ ext{Omega}$-deformed anti-self-dual gauge constraint and constructs explicit solutions describing anti-instanton worldlines in five dimensions.

Findings

Explicit solutions for anti-instanton worldlines were constructed.

The anti-self-dual constraint linearizes under a generalized 't Hooft ansatz.

Finite action configurations describe creation and annihilation of anti-instantons.

Abstract

We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an $SU(1,3)$ conformal symmetry. These actions have a Lagrange multiplier which imposes a novel $\Omega$-deformed anti-self-dual gauge field constraint. Using a generalised 't Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface.