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

Abstract

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. It was also known that the Haydys-Witten equations on product manifolds $M_5=M_4\times \mathbb{R}$ arise in the context of twisting the 5D maximally supersymmetric Yang-Mills theory. In this paper, we present the construction of twisted $N=2$ Yang-Mills theory on Sasaki-Einstein manifolds, and more generally on $K$-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys-Witten equation.

30 pages, the vanishing theorem is improved, refs added

References in corpus (7)

• Supersymmetric Gauge Theories on the Five-Sphere
• Instantons on the 5-sphere and M5-branes
• Factorization of 5D super Yang-Mills on $Y^{p,q}$ spaces
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone
• Moduli Spaces of Contact Instantons
• Note on a Cohomological Theory of Contact-Instanton and Invariants of Contact Structures

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