| Summary: | Abstract While studying supersymmetric G-gauge theories, one often observes that a zero-radius limit of the twisted partition function Ω G is computed by the partition function Z G $$ {\mathcal{Z}}^G $$ in one less dimensions. We show how this type of identification fails generically due to integrations over Wilson lines. Tracing the problem, physically, to saddles with reduced effective theories, we relate Ω G to a sum of distinct Z G $$ {\mathcal{Z}}^G $$ ’s and classify the latter, dubbed H-saddles. This explains why, in the context of pure Yang-Mills quantum mechanics, earlier estimates of the matrix integrals Z G $$ {\mathcal{Z}}^G $$ had failed to capture the recently constructed bulk index ℐ bulk G $$ {\mathrm{\mathcal{I}}}_{\mathrm{bulk}}^G $$ . The purported agreement between 4d and 5d instanton partition functions, despite such subtleties also present in the ADHM data, is explained.
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