Contact manifolds, contact instantons, and twistor geometry

Abstract

Recently, Källén & Zabzine computed the partition function of a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques. Key to their construction is a five-dimensional generalisation of the instanton equation to which they refer as the contact instanton equation.Subject of this article is the twistor construction of this equation when formulated on K-contact manifolds and the discussion of its integrability properties.We also present certain extensions to higher dimensions and supersymmetric generalisations.

M5-branes from gauge theories on the 5-sphere

“…The configurations solving this equation are called 'contact instantons' in some literatures, and recently studied on general contact manifolds, including S 5 [22,23]. In particular, [23] explores the twistor construction of this equation, which could probably be used to get a better understanding of its solutions. If the topological quantum number for these instantons on CP 2 is nonzero, one would get various non-perturbative corrections to the partition function.…”

The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

“…The first equation has been introduced in the context of topological 5D Yang-Mills theory in [5]. This equation can be written on any contact five-manifold and we refer to this equation as a contact instanton (these equations have been discussed in the recent work [32], see also [33] for a related system of equations, and also more references therein).…”

Instantons on Calabi–Yau cones

“…These torsionful Yang-Mills equations (3.12b), which arise in the context of non-integrable Gstructures (with intrinsic torsion), have been studied in the literature before [13][14][15][36][37][38]. In particular, the torsion term does not automatically vanish on instantons because dω contains (2, 1) and (1, 2)-forms.…”