Letters in Mathematical Physics

, Volume 106, Issue 1, pp 1–27 | Cite as

On Twisted N = 2 5D Super Yang–Mills Theory



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.


five-dimensional gauge theory contact geometry 

Mathematics Subject Classification

81T13 53D10 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Mathématiques, Université du LuxembourgLuxembourgLuxembourg
  2. 2.Max-Planck-Institut für MathematikBonnGermany
  3. 3.Department of Physics and AstronomyUppsala UniversityUppsalaSweden

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