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We study super Yang-Mills theories on five-dimensional Sasaki-Einsteinmanifolds. Using localisation techniques, we find that the contribution fromthe vector multiplet to the perturbative partition function can be calculatedby counting holomorphic functions on the associated Calabi-Yau cone. Thisobservation allows us to use standard techniques developed in the context ofquiver gauge theories to obtain explicit results for a number of examples;namely $S^5$, $T^{1,1}$, $Y^{7,3}$, $Y^{2,1}$, $Y^{2,0}$, and $Y^{4,0}$. Wefind complete agreement with previous results obtained by Qiu and Zabzine usingequivariant indices except for the orbifold limits $Y^{p,0}$ with $p > 1$.

Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone