On twisted N=2 5D super Yang-Mills theory

Understand

On a five dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries.

• The partition function of these theories localises on the contact instantons, however the contact instanton equations are not elliptic.
• It turns out that these equations can be embedded into the Haydys-Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa-Witten equations.
• We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems.