Abstract
We study 7D maximally supersymmetric Yang-Mills theory on 3-Sasakian manifolds. For manifolds whose hyper-Kähler cones are hypertoric we derive the perturbative part of the partition function. The answer involves a special function that counts integer lattice points in a rational convex polyhedral cone determined by hypertoric data. This also gives a more geometric structure to previous enumeration results of holomorphic functions in the literature. Based on physics intuition, we provide a factorisation result for such functions. The full proof of this factorisation using index calculations will be detailed in a forthcoming paper.
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Iakovidis, N., Qiu, J., Rocén, A. et al. 7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds. J. High Energ. Phys. 2020, 26 (2020). https://doi.org/10.1007/JHEP06(2020)026
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DOI: https://doi.org/10.1007/JHEP06(2020)026