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Twisted supersymmetric 5D Yang-Mills theory and contact geometry

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Abstract

We extend the localization calculation of the 3D Chern-Simons partition func- tion over Seifert manifolds to an analogous calculation in five dimensions. We construct a twisted version of N = 1 supersymmetric Yang-Mills theory defined on a circle bundle over a four dimensional symplectic manifold. The notion of contact geometry plays a crucial role in the construction and we suggest a generalization of the instanton equations to five- dimensional contact manifolds. Our main result is a calculation of the full perturbative partition function on S 5 for the twisted supersymmetric Yang-Mills theory with different Chern-Simons couplings. The final answer is given in terms of a matrix model. Our construction admits generalizations to higher dimensional contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov from the mid 90’s, and in a way it is covariantization of their ideas for a contact manifold.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala, Sweden

    Johan Källén & Maxim Zabzine

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  1. Johan Källén
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  2. Maxim Zabzine
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Correspondence to Johan Källén.

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ArXiv ePrint: 1202.1956

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Källén, J., Zabzine, M. Twisted supersymmetric 5D Yang-Mills theory and contact geometry. J. High Energ. Phys. 2012, 125 (2012). https://doi.org/10.1007/JHEP05(2012)125

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