Super-Yang-Mills theories on S4 x R

Abstract

We construct super-Yang-Mills theories on S4 x R, S4 x S1 and S4 x interval with the field content of maximal SYM, coupled to boundary degrees in the last case. These theories provide building blocks of the `5d uplifts' of gauge theories on S4, obtained by compactifying the 6d (2,0) theory. We pay special attention to the N=2* theory on S4. We also explain how to construct maximal SYM on S5 x R, and clarify when SYM theories can be put on S^n x R.

arXiv comment28 pages, no figures; v2. refs added, typos corrected, minor revision

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• A slow review of the AGT correspondence
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Exact Deconstruction of the 6D (2,0) Theory
• Rigid Supersymmetry from Conformal Supergravity in Five Dimensions
• The Enhancement of Supersymmetry in M-strings
• More on BPS States in N=4 Supersymmetric Yang-Mills Theory on R x S3
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Partially twisted superconformal M5 brane in R-symmetry gauge field backgrounds